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Problem 65

Algebra Difficulty 1.1 Multiple choice CEMC Fermat · Canada · 2026

The squares shown are each filled with a number so that the sum
of the numbers in every group of three consecutive squares is $24$ . What number appears in the square
marked with a question mark?

Pick one

Official solution

If the number in the square immediately right of $16$ is $x$ , then $5+16+x=24$ , and so $x=24-21=3$ . Notice that the 4th square
must be filled with the number in the first square to give $3+5+16=5+16+3=24$ . For the same reason,
the 5th square must be filled with the number in the 2nd square (which
is $5$ ) to give $5+16+3=16+3+5=24$ . Continuing in this way,
the 6th square is filled with $16$
and the number appearing in the square marked with a question mark is
$3$ . The completed diagram is shown
below.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.