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Lucy from the UK, Carla from Aiglon College Switzerland and Palestine and Neel from Zurich International School in Switzerland both sent in their solutions with an explanation of their strategy.
This is Neel's work on Difficulty 1, Puzzle 1. Click on the image to see it full size.
Carla also completed Difficulty 1, Puzzle 1 using a slightly different strategy. Click to see Carla's detailed solution:
Lucy successfully completed Difficulty 2, Puzzle 2. This is Lucy's strategy:
When I was stuck, I looked for all the different permutations that were possible to make the amount needed with the numbers which I still had left.
I did that for all the cages which I didn’t have an answer for and then looked for the most likely numbers and any which couldn’t fit. Once I had done that, everything fitted into place all at once, because as each piece went into place it narrowed down all the other options. It helped to view it in two ways: a number of small problems which is the cages, and separately see it as a bigger problem and look at it all together.
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?