What to do when in Cambridge

On Thursday, Alice and I were in Cambridge, at the University Open day. Towards the end of the day there was a students-only session, so I waited in the nearby buttery.

Daughter #2, the self-same daughter who had recently said the previously unuttered words 'that's cool' to a maths problem, had kindly given me a copy of her end of year maths quiz, and I took it with me on this visit. Many of them were fairly uninteresting, but two were nice. This blog is about the first of these.

Putting to one side that the diagram is hopelessly out of scale, my first method of solving, after intuition failed (I tried first to find an 'obvious solution) was some algebra.

Subtracting white from black (since the difference in these areas is sought), is 24-(B+C), which solves to 15.

I then looked for a neater solution.

In the extreme, the 5*5 square can be moved around, covering less or more of the 7*7 square. Imagine if it were moved so that it overlapped the larger square: with no outside black: and put the 3*3 square neatly in the opposite corner:

Then the difference between the white and black areas can seen simply to be 16-1, or 15: pretty.

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