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Challenge 337: The Last Number

The integers from 1 to 100 inclusive are written on a whiteboard.

Two students, Kay and Elly, take it in turns to choose two of the integers, write their sum on the whiteboard and then erase the original two numbers chosen. The process stops when there is only one number written on the whiteboard.

Kay goes first.

Who writes on the board last, and what is the last integer they write?

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.