Skip to main content
OlympiadHQ

Browse · harp

Print

imc

counting and probability intermediate

Problem

All the numbers are written in a array of squares, one number in each square, in such a way that if two numbers are consecutive then they occupy squares that share an edge. The numbers in the four corners add up to . What is the number in the center?
(A)
(B)
(C)
(D)
Solution
Consecutive numbers share an edge. That means that it is possible to walk from to by single steps north, south, east, or west. Consequently, the squares in the diagram with different shades have different parity: But since there are only four even numbers in the set, the five darker squares must contain the odd numbers, which sum to Therefore if the sum of the numbers in the corners is , the number in the center must be .
Final answer
C