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IMC 1999 — Keystage 3 (IWYMIC) — team Question 5

xIMC · IMC 1999 — Keystage 3 (IWYMIC) — team

Question 5

The diagram below shows a blank $5\times5$ table. Each cell is to be filled with one of $1,2,3,4,5$, so there is exactly one of each number in each row, each column and each of the two long diagonals. The score is the sum of the numbers in the four shaded cells. What is the highest possible score?

Question illustration