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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.