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Thoughts on the crossnumber

The deadline to enter the Chalkdust crossnumber #1 has now passed. The winners will be announced in next week’s blog post. In this blog post, Professor Kevin Buzzard shares some thoughts on the crossnumber.

In the rules we are told that there is a unique solution to the crossnumber. On the face of it this looks like an innocuous comment — a crossnumber for which this wasn’t true would be perhaps a little disappointing (or even unfair). However both existence and uniqueness of a solution to the crossnumber are not immediately obvious, and one has to hence decide what to do with this extra information. One could decide to verify it, by solving the puzzle and checking along the way that there is a unique solution. Alternatively, one could decide to use the information to help solve the puzzle! It is not clear to me if this is “cheating”. Let me give two examples to explain what I mean.
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Puzzles on square grids

Sudoku puzzles are incredibly popular with mathematicians and non-mathematicians alike. However once you have solved a few of them, or even written a program to solve them for you, then can become tedious.
But this does not mean an end to writing digits in boxes: as this blog post will reveal, there are a great number of other puzzles which revolve around arranging digits correctly.
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What makes a good puzzle?

Recently, mathematical puzzles have been hitting the headlines. First, there was the Vietnamese problem for eight-year-olds, which proved too difficult for many adults. Then Hannah’s Sweets, a question from this year’s GCSE exam, spread through Twitter like wildfire, leaving teenagers weeping in its wake.

Perhaps surprisingly to those teenagers, many people work on this sort of puzzle for fun. But what is it that makes a good puzzle?
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