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UKMT Senior Kangaroo, 2020

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

Margot writes the numbers $1,2,3,4,5,6,7$ and $8$ in the top row of a table, as shown. In the second row she plans to write the same set of numbers, in any order. Each number in the third row is obtained by finding the sum of the two numbers above it. In how many different ways can Margot complete row 2 so that every entry in row 3 is even?

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