Let’s begin with a puzzle:
![](data:image/png;base64,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)
I encountered this particular mathematical problem (by Peter Lijedahl) earlier this year at a meeting designed to provoke discussion, and expose elements, of ‘mathematical thinking’. The phrase ‘mathematical thinking’ is one that is used increasingly as something that we as educators and designers want to encourage, deepen, and develop in students - but it is very hard to quantify and observe. As we become more experienced problem solvers (and problem selectors!) we may forget what it’s like to be faced with a completely new mathematical problem and therefore the essential elements of early mathematical thinking which may be noticeable in our students.
So: it’s worth taking the time to examine our own thinking when we encounter new problems, to perform some forensic metacognition. If you can, spend five minutes reacting to the problem and a further five reflecting on your reaction.
Interestingly, when I did this, what I found particularly problematic about the problem above was that I didn’t like it!
I also came to that decision frighteningly quickly. Having read it through and established the ‘rules’ of the game, I was already dismissing it in my mind as ‘not my sort of problem’. This was only reinforced when I managed to convince myself (incorrectly, I might add) that it was impossible to devise a strategy in order to locate the treasure at all, let alone in 30 days. So, problem dismissed.
All was well until sharing and collaboration amongst our groups was encouraged. At this point one colleague proudly presented a representation of a strategy that informed her that it was possible to locate the treasure in the allotted time. Playing the role of your typical, sceptical student, I was unconvinced by her explanation. I couldn’t see how her solution dealt with the problems that I had encountered – but my curiosity was piqued enough to want to return to the problem in my own time later.
As is often the way, I didn’t return to it until several weeks later when another colleague, excited by the problem, wanted to discuss it with me. At this point something interesting happened. First of all, his excitement was infectious: he made me feel that there was more to the problem than I had first anticipated. Secondly, he didn’t care that I hadn’t got very far with the problem myself, he simply asked some questions, and encouraged (at times, forced) me to write some things down. His first question was simply: What if there were only four doors? My response was hesitant so he drew four lines on the board, to represent the four doors, and asked ‘what if you opened this door (pointing to the first door and drawing an X)?’
![](data:image/png;base64,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)
I began to respond verbally and he stopped me. He drew another set of four lines underneath and asked me to use these to record the possible places the treasure could now be (assuming that it was not initially behind that first door).
![](data:image/png;base64,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)
I was quite smug at this stage as the treasure could still be behind any one of the doors and so my initial scepticism was clearly justified. With limitless patience, he asked me what would happen if I opened a different door first instead. I selected the second door, reasoning that by symmetry I would then have dealt with all possible starting points.
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)
This was different. The treasure could now only be in three locations. Curiosity taking over, I continued using this representation to consider the effect of opening subsequent doors and then, substantially more interested, I disappeared to my office to work further on extending the problem.
Thinking back on this experience, it’s not the mathematical problem itself that is interesting, but the fascinating way in which I moved from dismissing it and essentially refusing to work on it, to a place where I found it interesting and successfully developed a strategy for a solution.
I was left wondering two things: what exactly was it that I had ‘seen’ in the problem that made me take an instant dislike to it, and what was it about the interventions of my colleagues that changed my mind? Students and teachers make snap judgements all the time about whether or not a mathematical problem is worth pursuing. As teachers and designers we attempt to provide interventions that will support and encourage pursuit of the problem without revealing too much, but this is inevitably a tricky business. What was striking to me was that it took so little to shift my attitude towards the problem, and in this case the most important step was finding a way of representing it that allowed all of the information to be stored on the page rather than in my head.
This leads me to another thought: I play an online version of Scrabble and recently noticed that there is a feature called ‘word strength’ that, when turned on will give you an indication of how good your proposed score is relative to your possible plays on the board.
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fuPLn2MO55QcVsc48VDptXOASOqmV2/kvwvg3NxHe8RLWj8crCgAIcyHjLS6pUx1RTDsXXBke+2hn1epiCI1/vjXkdUtTBFL0zGFUul/X1dHd2tHW2t3V2jFB7G5nUzmGzEAQZyssQ7zfL1M3v4OnnBRVpeWU7Tl44f+dJdV1z8YvaHy6FfLnOeaVD4HcXQpo7KPdj0vD+hxbjfL8x3/A44XlrB2W2+fr0/LIDv1z7xxLMDCOXgorXobFpqbmlf1+C+f5iyK3wxJColPLXDVW1TcfO/THLwnOmpdd0s02jaqqpp4HRhsvxhSrtO1HZUeLR8hSbmsvrFMnmSBoeyOhCuXZ3TO2a6y8sH9RbP2q2ftg0XI+arUIb192s9gh9QWH3B3AhsYjY0thF7qBTexi03lFF7aF0EJu7u8goiiAIumnvqW/M1y+03TTTxDUmNaeoqjYtrywpo/BedEp8en56QcXJi3dnGLusdAg4fu6PJiL5QewzfMChRVifL9c5f3fhTvzzgs8MsdcfxeWWvVxu57/7x8tlL9/s+/nqy/qW5fb+EU+zfvvj8eP45zFpuSUv6nb8eOW/Vjh/brxJ39RrdJls+tzYc9HxmJPpbQpYozspBp06glc2VpxkHXdgGT/aFKTbAQXjbgXNOKTeObHHJbHbJaHLJaF7hLpcErtdknrMQpuPpTQhCIpoNd1dJA6LDon4utDrqNLFMHu6SEIBDwDgufvHb0zdF2N9l9sHRjzNsvHau9w+4G7k01thibt+uGQXePhJcpYh3m+hrfc3Zut/vfHIbMPOBbbeS3C+35itDz554dzt8G/MNiy3C3gUn55TUl1YWeN74PRcS887Ecl5Za/S8srXugSdvfl464nzvgdOXwl7+ve1HgZm3pPNfUaVgZm3vqmX+ZV809DW6OoeAIBMKqGQ2vVAIQ4U4vp/EwdG/b68tI4TZQrS7YC4b3dGHzZ6Qu+cHeK73KPbWJASUStZDKpoAgHMgZ9djlaLeO7+QdefWErwX4TxXoTxXoTxWYjxXoLzXYz1XWDrtQTnu4zQ/6O20NbbEOe73D5Q10tYjPVdhPFZivdfhPGea+lp7LbdEO8319JzMdZ3ntVGY7ftizDeC2y8FmG8lxL859l4G5h5TbHwHQtWPy+TTRaXc/GJtEPPSSiKioU8HoepV3N5XfMtY0mSFSjEDY7N7H1sLksyR58RUIi6P5+LjSa5xFMcYsm2USTbKBImiuQUR3GJp+CiyfaxZJdBXnEU5zhyjwgGqGaCL7d1vGQSkVar3bjnx8H+15KB3pau39QPZUgXbAnOV9elGNZZ0/2/COO9GOsz+HEhxntxfw0+y+38F+D8J5l69XMx99E389E38zEwGyT1Di/7JNqujF4NgiqkYgGPpWc61cBsmoH38i+zflwJ8gZaWQ4WZFgiqQQAUfcXcLHRJPtYsn9qz4VK1s1XnF9LmfaxZLsY8pE8WlB6r30seXCQrmsCpRdSA6D9oICJQgYhCDKU18T79x/UuTfE+62wD1iICxikM93SZ6aN7ywbvy8sfXU7v7Acxou6J5uqQYFKIRXw2Hrxh5dd9Jxv9eXkdQb6lefXgEL8YH9iKC/rSNKlKjak1D7vEPUI4WySyDaKVMeQ363h2USS/qfwWoLzW2EfsADrb2DmY2DmPcnUe66t3yK8/zyM32J8wNfWvlMtfJcQAqda+BqYeY3OC7y0B5WEkC2LHOdOi9htCApxo/KyiSRdr2a/ostMwjs2JXexJKqj+bTSHskfr7i2n4jX0tF4DX36GXwYGnwqWGbnv8I+YIndFgMznxk2gdOt/RfiAw2dtv/DxHux0/YVTkEzMZvNN+6dZuGj+4kchVfdVSNBghXIx4E8rPa57dD+6jBe16rZNQw5LppsHt5Rx5DfesUpoEC3XnKtI/rHZP3lvBbj/Qzxfovw/ovw/ovxfrNxgYZ4v3nYgPm4gEU4//n4zbr7ve5etpTgb4j3W2EfaIj3W+20ZaVD4Ar7QCO37YZ4P6uNu1c5blnjHGS1cfcqx82WXvunWPgucNw512H7UsetRhv3fW7qvdR191q37bOxm619Dkyz9B2Tl8X0yRuXfnnKee6LC2tBPg5kYcfideMlu56lwESRjuZR+TL1jue9VX3Su6+5mL+0fS3F+y3A+8/BByzB+y3E+y/E+68jeK/De68m+Pg6uS7C+e1b77je2d3ddf3tLTZL7LaYe+xa4RBo7B5suXH3crsAG699ywj+lp67zTbsXOMcZOO1zxDvh/M7uMZ56xrnIIzP/tVOW6y8D0y18J3vuGOu/faljlvXee793NR77YY9q1y2z8RstvbePx6v3RYz7WZPXTNJ3/KLyU+PLu9/2TGCl24QPFOiLuuWUMVwaB3X8klnYRfUwVOW90ju13DxMeS/hNd8fIA7bsOPOLsVeN90OzNHvMddF5uzjviNTu6yoIXGBK8X21fHB5gd9LJvO7xsif0WrN+h1U5bTNfvwPgeWG4fYOO9b5mdv8UAL+tNew3xfljfAzpett77hvKaY799sX2Qlff+bzF+lpv2zSUEfWW72dr7wEJcwLcY3+nmXuaXRvBCMmy7w82ueM03m2awZd1XylQbkIMdycspjrIhqWtHZt+BHGpAWg8umuwYR/ZN6d6TTT2QS9ua3usYR3aII7skUHo+kJdEwAFqCQCo785jc0xdv8EHnsQ51GLXGuO9ZQ5Lggkuce4W15wwvs6umq0LzAhe5dvWJgaa7tvk8ObgyiX2WzC+B3W8bH32fyivefbbZ+K2LHffO93CZ4nLrpm4oK8wm1e47/3Syne6ufdk003ml3Ptk6i7s4be78sJ4I1jR4iJ1ZeT/Vd9JX9qPRjP0fHam8/BRpOc4ymOcRRCDJkQQ7aLJesGddvHknV7dF0KXfuiQmqAToiXiM/RQBwGi5HcyAh5IzL9Lmyu3bY5tptOYOxeYI3W4b35Dku3EFxj3SxuOGG8nN00W+ebErwqt6+OCzDbt8mh+dDyxSN42U6El08/r2/tt3+N2bLEdY++qfdil92zcEFfYTYbuu2dbOajb+qlb7rJ4kq+XSJ1Xw4VGeSVcnxF0pFlW42+XvnZpD8CF4J87OD7IW0qAUhpv1QKrCY2rBQTRdr+vFehQQCK6N4UjA9LJWYnvOlbfKdV70yj3plWvcuk//itbtruh3jchq0YpyV4v50EZyO8t4f9+g1269fYeR90dViG9w1wc3F02mDpuGnXRmdDu82rnbcuJfivdAhc5bjFEO+32nmLId5vpcPmFfaBywj+q522GOL91jgFLbcLWG4XsNppy3L7wDUu26Za+Ey3DvjC2n+qhe9XmEADM+8ZtoHTrfymWfp9ZRs42dzHwMzLwNTL6lqhdWzvtWo2AEAFKwU8lt46A/01+vr4b6be9FsoTbF5+2Cki6/K6S18rVM8xSay0zGO7BhHGUvYaJJ1ZKduDC4AQCGX6kY7jsVLLWan1Pf95+/N/+e3Rr0zDXrnG/XONPznpba/3eyeciByrq3XEpzPN7iAhTi/eVj/eTj/RTi/mZiAxTjfOZiAeVj/hVj/ufgtukDVYl0AFuuji8T2x2N1cX2szxKc7yLdR6zvEpzfMruAZXb+s218PzPxmmTqpW/mPcnUy8DMe5Kpl76pt75p/8fPjTw+N/Fad6NqUxq1WwQD3ahXkUCv/rpRw3Ujapg5KMC9HYz5bvzrNUO+O6tPN6nOaYQc4yiOceTAZz3ZZPHQ0IdCLhurlUmFHAaTMf9uq97Zxmqq7GQBQ+9k7VfXWhuZ8s3pNL3fWuduODrX2GmOhcdIzbbwmGPpOc9q4zzrTTrNtfLU7R9Hcyw85lp66sp/a73pW+uN0008/rZm/X+vHkX/tcr9b6vdlx96cLiQ1cJVDp4RgiB6oAgPivGgAAeyMP0aLV6o1qLdIjVZqKaIhossVFOEaqlKOzIKiKIIgmiRERsASBGZr3e2Ue/XhuD0PoUa+bmQUUOXVfVJZ1xt1jvTbH//ZVZF/fPKxozhasqobHxeVpdeUPksv3xQ6QUVmUXVWcWvsopeDlfxq8yil8PKP8svf15QnpZfnpJfkZpfOVQpeRUpeRWVDR1U2bsDEnXxLzQdM1wZGJA9WnwVUQO1EmjgUaRVjRIzBQAAAMOwUqmE4XekgpWhFWS9Mw16vzfpfVe7L4sKAOgVwf/xW4Perw1659odH9cqM3+XZV8ZKmn2FWnmJUXRXcBpH+1QajUCaRDJCEEIkI3l3tgbqnt/PpyXMho/VIpovCoeD9JwQ3nJZLIuCqmtpbG1uWEMNZI728Ui4dCq+TxuZ0fbqOV7iPV3sqr1fmvSO9vw9bWWaqqslaPkyjS7Mqh6v9TrnSN53kuUJhO4T904T904yW6cZFdOsisnyZWV5MJJcKFfM2MknUYGBi/zxIxnFbdC0nbfSg764+m2Edp6JyU4Ju+Xjt7XQ90T8HmkMdzTqa21qaebAivfXo9arVZPE2s/VNp4e8FDXOr+1YJwc/QZAUjpcljV3tbS10PmsOg8DoPLHi4em8FlM2h93cTWZqFQoKuay2G3tzUzaD2DBYZKwmM0dFA+v9L0f840vmHKa+jyv59t8HvaAwDYkNSjd6o94uklUL9TVXcArtsP1+6Ha/fBNXvh13tVNXvpBcHll3C9P8xmP78IABBArNDn++8894woCoou3R5dum2kokq2hWb73Ej21g38BADwuBxiaxOdOrp7XDaDx2FwWPSers7O9lYYVgIAUBTt7iLraePshwqJt1fH2uccW8e4Y4Gk2KESGp3JZjOo44RJB4OlPA6jr6cLQRC1WtXTRRbw2GNZiQVcJZ9+Ooeod6bZI7Fn2rUWvV8b9H6pd4jtmnufaXwlnZ+0QZvuDj/bAKeth9PWw6lucIor/NRFm+bWesMmxHex9I5xz1kjNY9e2BgVmrspuXp3YtXuxKpdYynpxe6o0s2R+UdValirQbopJAGX9d6TgkR8BrWHyaABAMQiUW83WQ+kOr1VipM2zh4kOVSdNmHdtdImOWjFfXyBSDSxnrpIwOWw6Gq1GoaVXBZ9/DGlYj6bS+/el9qqd7pB71SD3jmi3oUevV86jc8nt4Y4oWFmcLgNHG6jfmKjjbBRh1vDj63gx1bqMCvogWV8sKEi1IL22ypRa2n6m4txFVsn8iI9oWpHdEkwS0DRwFoOizGRIa868TgsFEVFQr6Ax9Kr/sVUp6rTpg3nzdUxdmi8He8BRvEEo0lw/NDxEwIeW6vVajUTmm8F8dkiZk9KdcvONJLrreyNv1wLuX6YG2KOPDaFw23gMGv1Exs43Eb60Er1xEb1xAYOt1GF20gfWjedM1Y+tmJeXCduK85qvhBbvlU3ECiqNCCyxD+yxD+qNCCufHt02ZahYzjiK3fElm9nComoFnzQGYmFfACATAoJeGw9/DdTMTOnmE7TX/nZZ16GX0jDcSDdA6RvQKKx6ngHVPKvnc8n4nOkPDoCK8Rl4bxfvgGPjbURNqpIrCoCq4nEaqJwVz0W+iybcXPTIjQGp4nEqiKw6kgsiMUpw2xZl4whYml2y6XY8q1xFdvTX5/spBd1Moo66IUkRmle/e8vO58kvzgwOCYhvmJHXEUwW9wBkA/jBYkFAACFXCrgsfVws6ZsWjrjiueii94rwvYYKyPxoGgL8nyjNgrzEXjppNAASW0q+9IqVTRBFWOnirZTRduBRIeOq5bYWVNMpuo7zpvWe8saJDrovlLH2Ckj8KyrZlB7mY5XfEVwSvWRKmIoW9QulPZVEUNz3vwmlPalvTo+OOzlr+FlPcPgMG4ByFgPqraB8q3IU1e0KAhJctFGfYz2pXNIrkZFNSnMK2vhOEdVgpMq3kkd7wTS3R5uWW7xhYHzt9PNphvE71kN0l1V8U6qeCd1gpMyxoF13RJqL8tuvjh4PYYVejb2pJGYJQ8L3FOqD/GgrrRXx/5iXjYzDA7iFiLZviDXF8n0RnL80LxAbZy9Nhr3EU5b4t4AACAASURBVHkhopo05nVjVZKr+qmbOtkNTXWXxjkHrZvpMn961M7VmJlT9lnOUSW7Iilu6mQ3zVM3OMGF9YeNuKN8kFdC5a6o0sCWvkwKqyKixDf15VEeREl5eSimPGhwpONfxgut2AWee2qfuoGqvUiWjzaG8LF51aYxbxqrnrqqU93UKW4g2+PFeSvjKZOOYOZJE102r5lpPWNy83UMyNygTnHTpLrBSS6sO6PwaqPmdHOqI0p8Ul8eFcloOfXn0l6dSKral1C586/jhZ2PFAaBp67aBEe0KAhJdf8kvFh/mKjT3DTp7tpn7iDX4+LGJSs/+yz7B1NQ7/9k1+rlf/9HyJYVIN9T+8xdm+6uSnFl37WF3uUVXbalhhzb3JseWeqf9GI/Q9DEEhLpgub8hguxZVv/Il5fTT5oNVsTaw8SHN7pu35kXnVprDum6ufumqz1IM+TE+vkaTjD+svJPzktDNm28hj+W6svDQJWz5SkuIIcD23WelW6G/s+Buosz2q6MMgroXJXYtWexKo9uv+TqvalvjyS+vJIUtVeXfuKrdjOErX/Fbxi7IbzisGpExxQCRWSfCivD57vLlcjojdpzHum6uz12jwPUOGVecrMYpq+8/zpDnOnYb6e4jhvmsPcadYzDEp/twblXto8D1WmO/shRkKqyGu5GlMW9LaTVbFzSAciOK4iOK4iePD+FV+xky/tAQiY+OkIBtIh9fMymaq/22zWKO0rBqtOskMlVJlCNfH57pBIoHvUEk04bRKfy1IhQFibQrttBGevR4s3IcUbD+HmrdX/PPG4MTPNjRbrxEx1u7Vlxap/fHZmwxJQ7oUWbVRmrqffs4R76t9Q0yOKfSY0ULY0MKvutBZRgw+Z5cDnsuQyKQBArYYFPLae77IZZ5wXaGLt0XgHbaz9oJBkG00KHpXQEBRMYGo4WzdgQq3un/mqgpXvK88W8Nh8Lqu/tTPaem5ZQskOoNyr5QHBePIkx3nT+KmuoNoHlHuBGt/WUDvTKfqYmVN6o51A2SZxon1vCF4rYis0sozaUxHFvrr5b7HlW0doW2z51shS//iKHXRB44e6JxbxdSPUAABSiVhPHUdQx9lpE4YokYCm4vrnp0mYujiGTAKJhfxxJJWINOp3hmSqVbAEEo1jAon4cpkEHfCGlX2h78YqeaoTLcYx5xeL2j+w2nxPTZ6HOs9Dk+8J52x4cdU251dzRqyjLMWh78ZqXsUjnaFcJXxNisqsPfW85oeMmh+HSbeztOUmW9T+rnuq8d0Ti/hymWQQFgAAoKgeyMKCLCzIwLyVbohhpo0mwVRDyR96DHQMjbONZTLSClHDnPxr1EduvAgHRbKzLNGJE2E/KG6kvTzJWZHszI1woD5ez698NDgSd+BAGg2i0CLKYdIgSi06fL73n95Gm+/en08Ug6aaa1LtNfW3tC2P3iuk5RFoe6xtefiuxi3f+hC0PkGE3YPeqGVievxPnectSOdNyefNyL+/I9J5M9I5E9IFa+azC4OZJHSbVqOViCViETSqIBGkgkeJACuVCpFQMKqEQgEkFmm1w0Osw/M9ohkYeri5cmDWFVrogJS7IGVO75W6xFGSQ9BOoKROaKUzNw3LDF2qSbTV0qoBAAo6kXLJkRaKF5buFJftEpfuhEp3QmU7odIdUOkOqGSHuDhYVBwMFW9nhVj33NqkEvTn4hTwecTWZmJr4ziZQdtaGhl06tt8oihCo/a2jZtPtK2lsb2tRTQQAQUAUPmy4fPdGREWWd+vKP51te7FGlq2Hq32Bi+83qPX3s1P7JJ+NAEvJ1D4hRd46SUt8nhxB5t+2lgQtgzJ8EBk/J67AbRfF8rKtilr9sEvd8PVu+DqnfCLnXDVTrhyB1wZDFds11QFk5/6pf1oxfz1W9qTfQDViiWSjrZmFoMqHEiCOaq4bAapo5U1mO6URiV3Enkc5jgmQj6HRe/rILZIJRIAgFSp3vykZlg+BYwszYZ83zT12HJUN8s2CwtyCMOVO6DBPXl2UDIm7/RqNPvd/WMpl6DNIfRFWJf+tlaWYgPSrIQZP3WdMYLumMKJTnCKG/zUFU52gZOc4UQnONERTnCA4+3hOHtNggP1rk345iWyENOeX1fIqa1MLm+C+USFfI4un6gKhvt6KINQxpFYyOOwaEw6FQCQ18YyC20ckg+mCA/KCeT7puW/rc4/vQoZhJhh+1bZGFCIAwVYkI8FBVhQiAPZGJBhC7IwcIpNxfk16HNbkGn7jkk+FhThQM6QenKxoASvfW6bfHgp8Y4xmo0Fz204IVjq7ybyh1aqx1bwY2skwgZE2qCRNmiETtbacGv4sZX6sZX4nkXCjqXKh5b0cyvFrSUCSPohkVJdPlH5xPOJigbSnT6qYdpEkvRAJgbkYcUJVk92Gd4LWtz1wIwWZaFIsenPsPCWGgbkYZFMTMHpVRc853/vMOd3j2/zTq3SZtiCfBzIxKAZGGWqzfC7YSYm4+SK+1sXd94z7R/smYdtuml8L2hxxskV7BhLdpQFkoEBz625D+zpl82Vj21UT2xVT2xZty16rpn1XjfvvW7ee82897q5+IE1iMWpI2wVj22Yty2Vj60ZF9dI2iskcuUHPH7w2Frth+cTFQkAAI/e8AZ4FeHvblm0+L8+C1z9FZRs3T83ZtjvZi5WmmL9s/PcdQb6Rgb69nOmGk3WX2ug/4PjHPHgEJVhVtlYNAOz1ejrxf/12fOTK/uncRXjI3cvXfAfn+2zmgUKcCAPC7IwIN2aF+rAvGYFR2DVUTgQTzjj/K3j3Gku86fbz5lqP2eqw5xpPstnJOxajsTiNdE4EItXhmMYl40k7ZUSxYfw+lPzkXU96sf1fJtIkh4oI3SGmNrNnmr15eTXl9b2J/8abcbHH/4LV/xjkv+qGaXn1jBjLMt/XxO4+qsV/5h0w28ByMe9fTH+Lq99VrOMJuvn/LSqv+YifPyBZWv19Y/jZ4McbP8b9XRr3kNH5k1bONpOHWsPkhxP4uetnay/zWjmaacFp+zn7zL9xvbrKabTDHKPrwNPndSx9spIAuOqiaTjo/PqCTP/xXXeys8mXdw4v39UwEhe+Th6uLnzt9OxM6e8uWYEKu1APg5UEppuGuO+meowdxo93Fx3Vf4zvFi3cap4J02iC0hz+8l+/vLPPks9tA7kbQCprmia6zm3RSs///zChsUg1VWT6ALHOjJvWEg6Kj/sevzneQWsmoH7Zqr7oumMCIu3gwuHqQhfc3md8WSDHWYz+0ebD1x9u8xnGk/WLzmzuj+L35/m9ciJdZegSnLVPHUHzzf85LBg+T8+Sz9mDMq8QbYHKPa65bfM8G9/v+23DGR6aJ66wwkuzD+sJJ1VH5sXduZUyy8mJx1e1n9/GYNX3s+r1hnoH8XOBlmYwWQ7IAtzgjB7rb5+zP6lo1zIH8TrsRPrHkH91FWb6g4yN/zkuMBo8qSfnRYkHzVKOrjubuByl/nT/VZ93RmCQzM2aFLdVEkurNtW0o/Py/brKTtMv4bTbN+ZEjOC18uLa40mG+w2nzmM117LWUaTDfJPrRqL117LWUaT9fNOveWVcHDZWn39o7h3eYU5sx7YqZ+5aZ+vB7kePzktsJphgJ05xfpLA6svDUym6JtN0/8jYDnI89A+d9c+d1elurJCrKWkj87L8svJPznNGf2GPagCXN8jM7s5UwnfTG27YwIq7UABDlTYdYSY2M+Zip81tfeh2SjXcjYW5GIPYb5ZPWnS06PLQJUdKMSBSkLo9sWrP9f/0XEuyB0YRPXMmhfmzHpkr85w12ZtAAWePzkvXPX5Zw+CV/ZGO3aF2VVetPY0/NLiC4PKi9agaKMuvsq6/1F5PXzDt4kk6Vl9Ofl7hzn9WcrH4pWFAXnYSxvnr/jH59tNvn59dR01wqLmutFO05kr/jHpvMe36FjmxfiHwYtXfTZpm/HXddeN+iIsaq6u8181Y/Xn+s+Or+hvcVkY8MyK+8ieGWavztmAFGwEZV4/uSxc/rd/PPvBFNT5g9JN4LXvVf9ly//290d71oBKb1DkDnIdxY9Mkd4XKKJRQlxIOJEu65/LJ8qWiIUAgKQ2oVVEp97yv39+wGbWe3hlYkAeTphodQQ7e42+vskUA9ysqaZTDNZM0j9o8w0/3qo/hcwoVlh2jGWwyddrJumbTTPAzppiMsVAd/N6O/YzCwNSrbjxQdT7OGXmeqRoI6j0Oum0YPF//i3xuDF46aMt8AQvvB/tWWP433+/vWUZqN7AytryKnZXwQ3f169e13RB1a29PC5bCfEE4545n8uSDOYTFQkmGDQWcFm6xDM9Itghlqx3Z/OizO9X9t9KxuGViQH5ONUzm4zvV/7oOHeX+awfHOc+P7kCTrMZ81d14FoWJVjHHVh2gjBnj+WsHxzmph5foUi16UechUXTTDUpDkpqfc99N2EsTpPvASq8znsZWs+Y/PyUGaj20RZ6girvgnOW+G+mXPVeFPro4vLvCqftLZ1zpGzO0cov9pfPPlLhfKWmtp2qhLjjRUqFfO2QdKcTySfK57KGTuJP7xDpgSJLkGcB0kzBs/cpzRRkmIF8C5Bprk0xBZnmIN8CZJi9z9YMZJqDfEvw3Eybatr/f4Y5eGaGppkiSavUUSs0bUkAAMGr+O5rawVRNvJ0F1GKMy/JSfrMFc52h7Pc4Cx3RYabLBWXdO/QpH2v5n1X93NKN/ZSw4ITL86mUazP1/7ntmK7SzV8gUAuFUsh0XBJxAq57J1I6UC6U6lENLogkUwCqWAleHfTQ3P8R0qb5avJ8H6rTB8k22/wW5DrD/L8Qe47Jki2nybT5x2rbD+0eDtaEowWb0dLtoPSYFAWDEqD0ZLtaMl2pHg7UrxNU35M21c+6I2o/hk9cjMjlMANsxNEOHDC7FmP7FiP7ViP7Thhdppoq9MXrvzX3jemZ15XdAoDHrSs/fllbTfkfbdpyt6yqfvKKkjQyKDgX7vp0bs7holN7VLLIaBVoio5qpIDtQJolGIek97dObLwoAQsGqqWA42i3wpVI0oJvziLHvuQEfeIET9CsQ+ZSRGyvuH5BxRSqLepqutNWVd9eVfDO+ISy48/LNffW/n5rtJz6V07w4n/N6jwdkGf//2WafvKpuwtiy9tF3DpDDp1uGhUgYA37EAIgha0MB6VkcLKR9HjclJEJaWNLhrOi0wmDVNHO7G9o10q72+KKABUGr2trZVE6qSQySPL60QktnV3d2sG4rcwn085f6rTz7U7wK070H1UUfxd27dtZGemDHojFAqIxDYSmdzV09PV3T1MHEbvg5w2/T1lk3aVnnpK9r/f8rfg4ouZPR5/NP739hKjX6obW4h9FCK5c6Ta2loau8idg+lOeRLlofg646vlxjerTW69HFXrrr+wvlEWXkkedE8kFOiNmkeTSe8bTKbK4bApnUQhjz2RfKJ0ah8AANFq+26cZwS4SI5slR7dNo5E+/y6At1Eda8AAAqFnNRJ5LDGzCcqFfNEAu6J6OaZhysWfvdi/omqmYcqlpx8Mfdo5ZpT1Xl1PRoZfxz3ertI1L4eXcs6/bx53d03TvFdLond44gQTTK99bKojQkAUCqVpI42vVF/RMVCHoveJxaLAAAMep9wYgk7RQIug9arAQCmU1l7/aSHg6AjW8eX5Og20c5N3AfXAQB8PpfDfE8+UYmIKxFyG0n08oau1x3MDqasrJ5S3dLXTWUqofeHWOnUXoCoe/kyx/Bmh/ju987wcUnosoroPJnRAVBUJOBxWPTReQn5HD6HKYXEAICJv6kW8jk8DksNgKabLNrnBx3aIt7nL97nBx0M7Ad0IAA6EgQdDoIOBEBHtkKHg6D9AeI9PtCt8wAAiUQ8kT6RWMBRQjyFmI3CUgCAAuLCEp5MPKEQK5/LAoj6DUNKiO5f1sg+loyLJuGjyQ4D60HZxZCdhiDDx1J2ZXRrEFQGiQQ89pi8Bvtp0Ack5OcI+RwEAKSXAu3zh45tl178SXbznOTng+I9PtDRbZIzx6AjW6Gj2yQ/H4IOB0HHgiVnj4v3+sluXwAAyOUTzWQv/CfyFwKgrWcr7WJ1c6HI3indh/Joh3JprgkUXDTJNYGy+VmPawJlEBk+mvzO/Md/ES/xzk2yG2cRkVDT3qKhUxUpMdCRbRpyh/TCj9KLP2lZdOjEDtm9K+qOVvEeH9nt3z8JL5tIUnyLkA6p65nydp5ifzZ1Q2LXG6bML7VnMOnBx+K1Y6P8wXVNDwU6sFl64zdEJJBeOa1urFNEPZCH3QEAyG6dU2anql6Uira4yO5c/FS88ilQZKPA8klnXLOAyFX6p3a385T+aZ+E1/1rGnI7tN9fFOSubqiVR4QonkbDFUVwSa6quUGREqOqeymPui8OcvuEvHLJ0KN6/tpH7f6pPVSx6kAOtYmt+ES8HlzXdLaJgtygw0FaFl1295L02q9aHlfdUCO7dU5D7dXS+iS/HhUHe35CXnkUKKSWuzCk7ZdSBlWk2pbe28xRuCVSzMI77GLILh+Rl6cs5DKqVMJl+RoSUd1cDx0Ogo4Ho2q1htgs3rUJEfC0DCp0IFC8y/tT8bKOJGWTxV0i+Fm7iA6p7tRw3BIobKmqtFeaQxYfyaPhY8gfi9ceX8lP+5VPo+CcNHn0A+joduhAIHRoi/zRLemNs+I9PvJ7V2V3L0EHAsR7fD4VL7tY8sFc6uN6XlQT/3gBTZcm6HIVO7KRH9Uk2JfdR4gh46PJu//lvHrI0P4A6OBm8S4v8S4v8R4f6NAWXRdMvMdHvM8fOrpNvNdXvNcPOrpNvMfnI/cn3gzwcomnEGLINgMLQ+luWLZRJN0eu9i316P2/bx4bF00Y+K8BDy2SMBDAUDYDOjIVujg5vf276EjW8U7N8kj7wMAlIoPyh/N0rknEQsn7p5QwAUApUvUbgldg3f08WUV0Xm6lAkAUCnlAi5rdF4CLkss4usWoIGViokviKTLJwoQRB4RItq2YbBZjal9fuL9/pqOFt1T53uzCgzCEgv73VPBSgF3gulOmXJp/6pF116wTcM7h63xOlL4GDImivSSJgMAIAgiFHD1BlY6Gio2JOJrhuS7lMukOi/HFlvAY0sl4rcDrCCx7N5V8V6//ktyDEHHd8BVxYMHUqtUusev8Y8lFr7jXn+6U+44JiwBjy2F3rongbVnypi46P5V2kbKOrLTJpLklkBJa38b0lGpYD2lUv6OFHIVrERHzPTWaDSwUjGOhg1e7bciNqtKc1UlOaqS3OEqzlG9KEF4w5cRR1FEBSuVCvlwx8Z1T6vVwEqFcmypR3OvniVPaxentovTRiilXZRNFtOg4aMS9UbW8r/bOJsehdzxjkgdPV3kwXWKdJtKraxueZ5ccjmp+GJS8aURuphUfLGoLkYsfSeGqVAo+nq7KaSO4YcYOBCF3MnlsIc1FpFQ0E0hkce26ukiQ9A7iS4QjVrwOpORdIGe8Bsj8fxwJZyjJ5zjFEWpxNyhVsoJuMdhM4dF/fWovV3D1E3paGtp5HH7rxQFLI0v+u1a8oZ7mT4PsnxH1f0sn5spHqHP97MFvTorCBIRW5sppPaR9Q+qt5vc3tbc3UUZfG3DZNCIrU09XaRxrLopncTWJi6HrTPRqhTMxHPMc46iq+7QtQ2jSnxtPfd3R+rdnUpOn85KKpEQW5ve615HW3NPF0mrRQbco48SX4VEfD6XRSF1KJVKAEBZQ3xIhmfSi/esvJRcvfthnvfT0vMIgiBapJtCGidSOlQ9XZ1cDgcAIJFAXeQO4XtXXhLxBTw2hdSuUCgAAMLKJPFFJ/BoM3gcBB6NrcdByutunPhfUQTRImh3F5nNpOnSnY6v3m4Sh80CAMhkUnJn++j9Cd3MdbFYDABIe/FLzECu+vdPKC/eJZSy1CoNi0GdyIJIum4Rh80EAAj4XC57QtPQRQIul0UXi8UoikrjfwQhXujDLe8VCA1QPAjSiFiKD3FPyOdwWAwAgIDP43GYY8dXuSyZVAoAyHlzVjehKb5iR3Tp5n6VbY6r2B5TFjRsQnlc+Q6+pAcg4IPyieomlEsnFl8d7ILJ5HKAaLXxJ9B7fug9H/SuV7/u+aAhPmjoZjQ0EA3xQR9uQR8EoCE+aGgg8jAI5VBgBP2w9ZoEPBQFEkgs4I3RX9V1Z3TLfubW/xZTFhRXEfzs1YnXpKjqjsfVHY9fk6Iya38uaLykm4o5OOE3oXKXUNYH0A+bMKdbv1Yuk3zY85ASBogWTTyJhnij2VfRskdowR207BGacx1NP48+2oqG70SfnUUfBKARe9CMi+iDAPRREOB1qz/QvXfm802QV2z5tqy6012sSqmSJ1VyScyyirZ7Yjnzec0PseXbPimv79C7XujLBJTahKphtOcN+ioJ5VPRhBNo1mWgUqJhwWjJQ5TRjoZ4fzxeOhzhhZ5EWj6Rlhua75pR86NUyf034HUSveeL3vZEow+gnG40LBi94YJ21aBF99EXMahajaacBm1FaE0K+scG9NHWj8croXJXdGlgB72og174pNg7s/aURMFOf/19TNnWT8/rvh+acALl9qDRB9A/1qPV8SipGm3OR5sLQHMe6GtCsy6jdzw/Aa9ORkkno1jHS6rkptd8H1MWlDAwgfUT8+L3odEH0Due6LOzQMJHSS/QpB+AmA24PWj4TvSe7yfgRaTlEWl5T4p90l9/L1MKOOJOuqAxq+6X2PJtn5hX/HGURUaj9qP3fNCwYCAVguY89I8NgNcLumrREG/0gf/H5hVfsePZqxPPXn8XVxGcWLUnp/634ubrxc3XU6oPx1fsGODV+7Hv9/d80dDN6OPtaMJ36KOt6MMtaGggmngSjdrf3+6iD6IPAtAHAeijrYDX9a/llfPmzNAJ5XEVwXEV2xMqdydU7owp26pbCFNHaoAX9WPxUgIUQZO+R+/5oA+3oKGb0fu+6MPN/R3Ue77oA3/0YRB63xe9748+DOrnxe/91/DisbVqNQCgtOWPyBL/ifTvY8qC0l9/p9LIAQp0NUzIIS5LJpUAXWDyQ3q5arUKAIDm30Zve0ykf4+GeKMxh4BajgAwwcCkcGAhUzCYT3TUQv1Lx6MAAMARdcSV74gqDdRdcWMppjwossS/g16oezSVy96TT3QQllDA1Wo0AAAURSY4rHTAPRQAgLLJ6KMg9M5GNDRwPIX4oLc90Obc/iCCXDZR9/gcXWyyP5/o8EI8jpCvW3npbRyDxq/PrP15AM3OEdoRVxGc9upYO61g0ARFUYVcKhJwheOtL8uGRIKhgUZEq5VCovfykknF74RZqE1o8o8DaDaPogeBaNR+tCnnrXtv052OdyBIJNC14kH39LQazTAhIyYtAwA0Wlgso4tkNJGMPkI0kYymVEtGWiEIMrL+t9JqRpoAALTasU3GcA9o1UBAAwLqmFL8KfdGzMr/3/jqh216g7PoxR+i0efhj6EPqvmf10Qdg8Q6SQYlEUslkE4ynaSSYdIbLCGZsKQSSApBEgiSQpBUIhn8XzKWxq5ntI/iP6sxXH1H4hF7IKkUkkkH0MgkMplELpMOkWxQCrnsf6/HD9v+DC9SZyeJRAIAdHVRXla/kEgkAAAajQoPjO5HEASGlRqNBobHTCyi1WppNNrgR6lUSmxrk8tkI1Nk/Fttf4ZXXW1tXW0tBEHZWVnd3d26n/aG+jcCgaCnu4dE6qT29ZWUFDc3N1dUlEskkrbWVjqdxufziMQ2Eqmzs6NDo9FotdrmpkaZTEZsa2PQ6bU1r1+/flVaUtxOJL7XgU+4/RleYrG4s6Ojr7f31cuXHR3t7e1EAEBHO/FNXW1RYUHN69cvq6uJRGJfX287kfiy+kXN61e1NTXV1dVtba2vXr3s6GjXarUIgnR2dLyoqnz5svrly+oXVZV0Ou1NXR2bxfqrz/Gv3P4MLwqZXFFezuVyGxsaent6mhobAQAtLc01r19XVVXS6XQ2i9XQUM+g0xsb6+tqa9paW7hcTjuxTcDnc7nc4qJCDocDAGhqbHz16mVzcxOHw2lpbhYIBM3NTV1dXX/xKf6l2wfzQlGUTCY11L9RKpU0KrWpsUF3kxLw+WKxmEalthPbVCoVnUbTfYQgqK2tlU6jSSUSFQzTabSO9naVSgUAYLNYUqm0nUikUqlisVgFwxKJhErt++vP8q/b/vf38cO2/+X1YdtbXhqpUFSbJaxMFL1IHkfCqiThq2cwnzayLllXg6AyWViV9N4aJG0VI/OlaeRiUV32hBx4mQpzev6FVMbe+nmJG3IpFwg9103pT+yYTwjMiAE9GSo8IxzPjbZnh1pTzlnySsIHa9HKxbSYE+SzRtRQDGP0GvDMJwRGOJ4VQeBH2/VdNu4JCVSy3k79gpqLKBftu6+Z0gcPN5oDzCd4ejiBeteq53cLbv69j01LxwtqLW0/voh510pWf1TRekLZclzZclzZckzZfEzZdEzZdFTZdFTZeETZeETdcrQjc9urGH9OGJ50bA6v7AkAANGoeh/tJp+YLcwJkBNPKltOKJuPK1uOK5t1Nbw1VzUdEb8+UBnp15XsQ/9tCeWivUrIBABIOirbTyxh3DKTvjmiaP1uwIHjIxw4rGw4rGw4LHy5nxKCpRz7hpMf8rF5ISpl13V36s8LJUnuyrJtyqLNysJAZWEgXBAA5/vD+f5wnh+c5wvn+mryffmpntmnLKMPGr+6YC26uppy1lQjE4nrszuPzeHdMpPnByhLgvprKAiAC3Tm/nCeH5zrC+f6oIV+b27bp39nGnPYlHfPpveHueznlxA13H3bm3pqARTnoizdpizarCwa4UCuL5zrC+f4qHJ81Lk+CSfMUw+vk95aR/5lnZLZ+VF5KRid5J+WCW6aKMNt4ERHOMERju9PTgbH2cGxdnCsHRxDgKPxcDROFYWj37XOObam75qp4r5Fz8+Lha9S6Qk/Qd/h8gAAF3JJREFUUn9dIr1nDscQ4CQnOMEBjneA4+zhOPt+81gCHI2Ho3DqaJw0HFN33qz4u9XyUEvuldW9f3jIepspZ435N4yUYTZwwrsODB49Bq+rAY7CaWNw5Kvm+UdWqh9Z9p5aIHgR91F5yftaes+uhkLMdQs+wI+t1GHW6vAhCrNWhVnBj6204da82+a3POeXHF8JPbBUPLSinTXk5N6mhu1mX1qleNhvrhpmHm6tCutfTQJE2RQcWXHPZyH5sgkcZi28ZUy95Solv+49byq+awY/th704a0z/TW83aN9Yt131ST/yEokwob26yJBecRH5aWgtvadXyu5bwmH244q9RNbEIsF8TgkEiO6b133q1Hdr0bcECs4zJZ+bhk3/x49Yh/36hplmM1YNSCRGBCPA9FYdQSGcsWs5hej1t9NlGG24tumtDvuUkot9aK55L7FWObDpHpiK3lozblrCYfZMn5bIqyM/Li8aG20C0ayhzaqCCwSjROF2p7AzNlhNHOP6azdprN2mcw8ZDX7yvoFecfWaKNwIA4P4vAgnoBE4xRhGMbvK7gF9+lR+3nX18FPsKoILJpIeH5wVeDKr/aYztpjOmu3yaw9prNO2c17GGjYdd0CJBBALB7EE0AsXhWJhe6a0UM2SCm19MsWslBrVQR2qNBYPOmK+U7jmYErvyo6sQZNJAx+pY7EoTE4RTiGed5QWBn10XldMpGFYVTRBDTOjv8Qu37RFxZfTrb8crLRFH2jKfrrJk9aazDJ4svJP9t/C4XjkDg7VRRBHUNQRuAZF1dxC+7Tow7wb5moogiqaAJIdQzfumyV/iTbr6eYTNPX1bDGYJLRVH2X+dMLvlsHkh1U0QSdoPuW9HseUkot/aqV7DFmcL9OING+6XdzqxmTV+lPerp3FUhxHPqtOoagjMQzLy4XVn18XlfM5BF4VbwDmugoCCN4L/vK4guDQ9ZzMo8bpRxc82jbip0ms6y/mmwyVf/6xsXgqbMmzkEd76CMtmdeWcstvE+POcS/baaKc1DFOYB0l6gdK02n6TvNmxYRvDLjqFHCntWXPBY7fzvN4svJjvOmt1+3Rp866wpDD23oDzZKKbX0GzayJzhVvINuf39VKc4tl60Is6eaTTdIO7QGPHMZ+q063kEZY8+8vEr4Ivqj87pmoYh2UCe5gBRXYYSDz7KvjCZPuumzFBR4gnR3kLVeHO2032qO5ZeTHedNI/+BBWlumiQXOM6Zdc2YW/SAEXNIEGKpTnBWJ7qAzPXRu1YbT53k/O10bpg9yN4AnruD7A35P5jZzZ5qOk3/osdi8Mxdk+SiTnSRPMYyHnpJu+roNzHyKHt1kos68a3AM/fWq7Y6Xs+OrAOZ64d+q0lygeOdWdfWCl/EfFxe9DbaTStFnJM6xQ08cxdGO/ks/8p4yqSrXoYgy0Pz1E2d7AZyPavOWtp8Ndl8ukHGCROQ5aFJcYMTXVk3TLjFoYy4w4IH1uokV/VTN5DjGb17jfGUSc7fTu99QADp69VP3ZBUd5C+/qDNXOMpk3aYfKNKckVS3dVP3SRP8IxH3tKuOvofOHmsozrFTf30rUDGhtYbWMLsqWbT9Z8dNQY5HkO/1aS4wUmu/6+YM39r6swXeP4Bl1q9tXecsQqBBLKRBdxQAVHWBBCwtXamM7e3nZnbqiiQ7WQjQFizsUMBhbILCassijtr9g0CsoQdWrdaFYSZc39IgAAR7dyON8/n4XmT95yX8Hm+2/mF6VTs44737mtCcPhlqc9iTQBYG/ik2CfceTfO7KspaKk6YLE6AKwnPczw9N230+3DrUXfYMCmoKWagPlK/2kBYe5m9mTp+UfZR15f81+sDgBbgou+sfgy5XiB9cRF8wmNpKQwGOGDreGI3bOFJ8Fa4mJ1wPMrnpN5Yc+HZJMij5clpxZrAswXW25pIOn4x71+v8Ptw62SCDzYHGS9u1QTsFDpP8PHPul8/76ER16W+y5JA8F60pMS33Dn3bjtW5LCYGBz8JIkcFESCDaSRnNOBEJ3uX64tfBrNNgctCQNnL8WMC1ynbuZPVl24VGu++uagEVJINgWUvS3ZV95J8BG0qL5hOagjD8iXHdsDXXaPV14EmwgLUoCnxd5TeaHPx+STaZ5viz3WZQGmi+23NIUpBMu+7qEB1uDrXeXpIEL1QEzQtyTzh/esy/DRJr7y2t+iw1E8Hrwkwo/i68zcLAtZKmeuFhHBG+EGDI8vfbscN2xVRJFAG+eXmogzkuJ0+kH5m5lT5ZfeJR/9HVd4GI9EWw/XfR3F4uvfG+wJWixnrhUTwRvhDD87XHbtvyZ8LtXksB/NgYt1hN/LjkxWXDm+bBsMsPzRZXfYj3RGrAlWJfmYfEVRQDbT1vvLjUQ56WBM2mEJ13v2dekYSLd/aXEb/E6CWwNfnLNPxyxG7ttS+pZJ/BBONgWArafBu+Hpf0JcXDnVo/ffaAWe4DtIUvXSfN1xOmMA3O3sicrLvxUePR1I3GxiQTeDS361gW/fYvvvp3TpT7gnVCwLQS8HzZZ7BMC/wi/fQvgbw/eDPnH9aDFJtLPZd6ThWeeD8smsrxeVPstNpGsAW+G6DI8vfbscPtwq4TsCt4Ntd5duk6arwucziA86X7f8aUfSz/8QuK/1BoMtp9+Kg0MR+wmbN8aE+w4WxMwVeY7XHQq92v0id/vwG/fEnXS7h83Q/7ZFrLUGjzfQJzKcJttz5ooO/9j4dHX10lLrcFgZ3jxeRxh+xaffTvl4uMzVX7T5X6d/GPfHP7DoV3bjny0vSPlKHgvbKk1eLEl6Fm590Rh+POh3vFMz19q/JZagpdaVwHvhupzTnjt2eG2Y6uU6gZ2hFvvLrUFzzcSpzPwj7veb/1amH04nHrwaYXPYksQeOv0U2ngafhH7h9t9977YYDdLn/7Xaf2fkjYvgW3bcun6N3DRafAO6Hmb/xCEjAudn2mqpuuZ09lHnhVT1xqCwa7wq9+h8Nt2+K1Z4fv/p3+drv87Xcd3b0du3XLwZ3bsv8bBd4O/UdbyFJb8MJ10qMij4mr515N6E1iz6flp163BC21rfGlyz5x7OMPcNu2SCg2fL2oDRgX4Z/Jr739r/wNfb18/vNI7pnZnMMvawPBmyHPagPPYf/TZ/9Of/tdvvt3+u7f6We38zP0x/xzztPlfuA9i6z5BtKjIs+RtBO/PJ79UV43kuzytMJnoYkEdoSXRuCPffxBIHSX3/6d5hOI0P/49vgnTeyD4K3T4M3TS63Br5uDnkv8J9NwU9eTXr6aH83/Yib74IvawMWWILOLpbZg8G5oX563n93OYx9/UA8cMP9jvhWh8w3Exz94jYqPPzVp5xcW5t/XC9LcfvdOqWAk5cDjKx6/SPxf1AWaik6NXDk5enWVR1V+4O3T4I3ghUbSfAPxF2nA0xLvSSGh4wr9evv9luZmpfizmXTXp+U+r+qJP1X6DRV6W98+XnxqoYkE3jm92Bw030h6WUf8ucrvp7zD/cJTbXWVzbc7b5eLh1IOPio49rzG/1U9caGJ9LqJ9LqZ9Etd4MiVk8OF3k+q/V83B71uIi00keYbiC+kAU9LvSdFhK6CqOabd1pb21rf1wsilUqlDddvFSUYBadmM92fFHq8KvNeqPCer/BeqLAsXpZ5Pyv2elbk9bTI60mhx1yO+0OR5/0CqrS+SSKtldQ1NkqqZJl/MYncf8o7+rz4xELFyYXl2xcqTs6Xe/9ScuJZkdezIq+nV7we5R+bTHfXpIU2V+ZL6pulEqm0obm9OKVP4DOT5f64wOPZVS/zxc9/MB91cvX2Iq/HhR4/5h4dEnk8+D66tq5RUlsnfY8vSHVVRXlZSXZePj8WEEV+Lrh0hh8RnhoRlhoRlnoxLPVimGUdEc6PCBdcOiOK/Ewc9Xkq67I4Pau4+GpVRVlleWnh1SKhUCig/VV46UxqRHjqxbCUi2GpF8NSLoamXAwzYz5EcPlTUeSnAsqfU5N4ud8XVJSVVFWWl5YUZ+V+nxrLEEae418KT40ISzFzMXTlBPPX4F8KF17+VBR5NoVxUSTOuHrlSmV56TtSUfarKLEJJCuvMCu3IC0rLyUtO46fFZOczklKYyemsRPFrASRBZ6IlSBmJ4jZiWkxyemxqVlJwixhWlZ69vcZOfkZOfnizFy+OJPHz+QkpbESREyekBEvsBAnYMQJGPFCJk/I5IlYCWJOUlpsakayMEOYnp2WlZeenZeWmStIy0oUZMQkpzN5Ika8kBEvAOIEQBwfiOUDsXwgjm8+jckTshJEnKS0+NT0FGG6MD1bnJkrzswRZ+aIMtYjtkKUkSPKyH5nNp5m2YIgyXeR5Hsoyj009T6G9gBD78DQO1wsdG7AsoWhPUDTHqCp91GUeyjKffO9LvQOLNC5TBcO6MQxutYDdFkuoHe40B5gljHfi2N04RndeEY3nmmBsAye2Y1n9qx8jmd04Sy/qAMLdGCBTiy9E0vvtPoCnbj1dOGA1W+C34xughnmeiB7L3ftvdz9SeQbiOr+JLJ7X1TPG4nu2W+hdx12FmR2ZJkdudeOLLPGniy3J8vszQuKBegaFKtQFVCqwsEGSgs0paNtVGZg9E1Qw4HNcALUTgyNGYh9VNd6oi1Ao7ttQ+6GkrsdLPTYgNLjuEqvDai9sDXIrIGboVkjt8aJJneib0RhxnkFYCNKhDWM9SAZqjUw14BiqiD20d3Q6C7oRjvkbmh0t0P0ipdVO1ByDzS6B0q2gQO5d9larwPFBo6UXkeKbNmabIVVWct2zFIsiw2CzEbeZAcBKBCA0nlFylo7SIYKaW2HucYOiqlCWS1QTDWKpUYx1SimGs1SQ9ZFDXSTqCH3QMk9f7jUtS+yG0HvRQIyFCBDMeRohhyzAtMahRkXptyFqbDAso35SieafF9UrwNF9ltHzWaBs+rFGpYF9Bo0kE3sWKVVL4zSuz+qB0ruOZNpYFSPcKSjHOloTO1ojHQ0ptbEXUfdOsZWiN3A6m7tGLfOdKF06FCcen+07P/RjhOgsqco7ShKR7oKzdKgWRo0W4NmazBsDeRdig6M2rsvsgfPVrAlo98WDx7nqZGA3Ikmg9NkMKpsbaLJHCky60Rbl24wqhxGlcNoq8Bpcie6AgEokAyFG1cdntkfWzf2eY7Rjix3BhSIX1tx/g+xg2ZpMGyNI03lmWxg144nNU2ey3sIo6vMpjBsLYathWwsxrANxRhK7kXQZbF1pgCBbk9Et1107xoLb6jKcJocTpfD31CVVwEslciJroDTFPuj5QhAyak1nc0x2pHlv6oYr1fDsqlGswp7NXDMwAG1n7C/vPun86Wj5/Ie5t+b/a5kBEpTo1gaF47WhaOFbN6qzAX4k8ieS2VDn2X37bnUbRYBo8kdqTInmiVYoBSZA0XmSJXB6XIYTe5AtcwEcJrCGVA40RUOFLkjVW5ew2gKBKCAW9JNCacrnAGlI00BoynMXmA0BZKpjG8YPxKvhdOV/z47GKvAwbC1KJYWBqizb8+czR3cG620o6qP8PQSxWM/odEtVo9ha104Oojtdm7Vy6EUmXu8mlkzCiX3rnQrBCB3BuQOFBmKoUAAimMJGo9ELZ6jglJkaKbyWIL2eKLWM0mL46gcqQoYTXEyVefO0zoBCgRDiWapnOgKDEvlDCidACWGpUIxVZ7JOs8kHZKhQjBUSKbKjqL4PGfgfMmwPUWxSWah35xZaJYG8w6OMGwthqN14WgxbC2eqzuSoM9onznE07twtEimVtA6nd4+803RcHHHjwSuHsPRQWzOONYtfH9079mc/i9yjXsje81Z40CRH+Vpqnp+xLJVX18Z/PaHIWHr5Oc5xoulQ99cfUipGvlLwWBp11xi04Q7T+tAVbClpsSmiciKUThdeSbLWNI5t+eyLO/OzH8VPPQTGDJuTp/LHRDfmP4yf3C5kasRDJUrV0OpGsWw1EjmZlKsi/EbjbC15mzagG4FFEt7PLnv+7tzNwxPxTdmcFwdNkaXe2cOG6OHM7QF9+aOJvZhYvQQm46sy409Wf5pVn+A0AAly80dCkqReyZp65SPGDWjURUjQI0p9/aMd4oew1J2Pvz5Qunwrgs9nNoxX4Fhz2XZudyBrPbp312S+fINGJaaKTFV9f54iq/PvzuTd2cmoXE8+9Z0RNlIzu0Z71SDE7A67yCYaqZ07FC8Dsn81Zn1Lo6wHB02Zg1whvZ86ejYo/kvC4bhDC02Rn+146dz3w8HpQ9W9D46ktDnEqOHvHVEhlLkZ7L6/fh6B6rcGVA6A0ooReEnMAA1o5fKh9v0T6IrR0RtU+48rS9fL1U8ol4b3Rsli2uYIIr7PomSh2YYC+7N2lMUgtZJTu1Ywb3ZwvuzCY3jtGqTsHWK3zIZXTnKlo7zW6c8kvQIhiV8UCw1gqlh144f5umR/3oE6bBvtoON0eFidNgYPTZGj4vR42L0WK7eJUbvldKPYutwXD2KpTtfZsq4NZvWPsuUTmBjDDiuAfLWMceeLP8id8C6W8FoCq9k3d+Lh5zoSkHL1F8KHhbcm2VJxmLqxryS9VEVI+487d+Kh06lGmB0JZyuulg2kn1rWtQ2FVc/cTZnAMVUAzUmarXpYJwWx9H8tWjou5KRKw/m2NIxAleLZGowbA2KpcHHaKjVYwSuFs2yUW42yayNXpZZVYPj2sSA4+rRbD2ea8DHGvCxBgRLh2TpkGy9M0uHjzUQYg2Qtw6BjlSFv9AQXTliT1as9HIEQ+UMqJwBlQNV4cxQubDVbrEaFFMNp6ucGSoMS+3MUJnzCMlUO9KUB2K1aJYawVAjGGoEU41gqlFMDdK8YGmQTDWBqz0Qp1sJHDigDkozRlWaYID632cHzzUQYg3OTJ0joMVw9AiWHsbQucTo0Rw9jKFDc/T42D5nlh4fa0BzDPjYPhy3D2ItCMlQIjeMyAiGCkZXcuvGffgGKEWBYqqXn7DUKKYaaYZhWawUZtRKVWZr0CwNiqlBLZceDNvyoXVaoVkatFWrggFqdu0EKX3AmaGxZNMb7OAs6HFvsIPn6vHLdizEroLm6L+6OhrXOOXNN35ZOMJtmPITDQZlPExunj6XN4zjGr66Muoa1xeWPXQ0yeiRMgBZ//TAXH7+tOriMLrSM0mf2DThGqOBUpXrhh3Umoaltm5Ya+vO+nKD4dioO0iW1oGu+Z8fRiIrTHBA8/aosSHI7EVv7WUFQqyBENtnIa4PxTYIb8xwG6biGqfS22fJ1ybO5g6Lbsz+MX8kOHPIXzzYonvmIxzkNU0Hpj8MyxmCvMsQiGapHWjK4PT+pKbJ0Ewjkql2oKmsga5960BTOdDUDjS14wr0jWhgZgANDNDAAQ0c0DgztMcSDbTqcXrNOMYSUJvnlN5m1Ky1Y1ixsxEU2yC6MVslexxRMS5om42smvim2MSsnfw4UrOfpotrnG7VP4ttmGbXTXmlDgZnDkHeYUS2xI4DTXUsUc+QjFGvmSLKRiMrTVGVpqgq88+xqCpTVJV5MRb9Vq6NRV8bI1+zrMlVY9FVY5GVY5crxuIaJr8sGEawdBiO7re147pKv2tcv2t8v2t8vwu3jyGd/Lp4lFw9wW+bSbg+cy5/RNA2y22YJl+bSG6Z+aJglHd9Ouv2nKBt7kLZOGTzp4d1LdyZoYHR1Ud4eh9Bv6+g30/Y7y/s9xeZMW4kQGQMEFszECAeWFkEWt5a8BcPnBIYcVy9M1P3bmr63qam31rNCm5WuMb3H0secI03eqQM+ooefllo8uIPHk0a+KrIFJQxfDRpAMXpO5w44J829KdCk594CLLpBKi1OeOgWFokU7OM1gLLBigLOhRLh2KvB72KHs3WYzh6DEePsyXot7LjFm90ize68VY5wDMS4oxu8UZCvBEfZ3Th9rvGG13jjS7cfnyc0ZU3cDBhwI03QIgzYmONrvFGiM0h0GUFW8MOdrlh2RwCse/QrfBvCB/CetY4crXBqiO3N2J0izce4G3CwAHewMGEzTiUMHgocfBQ4uD/AlTjySm5zmxQAAAAAElFTkSuQmCCAA==)
Since activating it, I have spent considerably longer searching for words that will at least score into the green end of the scale, where previously I would have just submitted a lower scoring word. The word strength feature doesn’t tell me where to go; it just tells me if it’s possible for me to do much better. That’s enough for me to have significantly improved my resilience in looking for good plays and therefore my success in the game. The realms of possibility have been sketched out for me so I have some sort of mental satnav for the problem – for me, immensely helpful in scoping for my own expectations for solutions and consequently allocating mental resources. How might we do this with mathematical problems? What might it look like?
Can you think of a mathematical problem that you have immediately dismissed as ‘not my sort of thing’? What do you think it would it take for you to pick it up again?