don steward
mathematics teaching 10 ~ 16

Saturday, 8 January 2011

unlucky sum

using the digits 1 to 9, each used once only, can you make all (four) of the lines of 3 squares sum to 13?

this task can involve some thinking, after an initial exploration - helped by having digits to move around

the sum of 1 to 9 is 45 and four lines of 13 equal 52 so the additional 7 must come from those squares counted twice
there is only one way for the three digits to be placed and the rest follows

ignoring swapping the digits around at the ends there is one solution to this task

exploring other line totals is an obvious development:
there are five ways for line totals of 14 and 16
one way with a line total of 17
other line totals are impossible - easily proved for a line total of 15

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