Maths Olympiad Prep

Track / Stage 4 / 248 of 340 #508 of 1964

Problem 508

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

Fill in the squares with the numbers 1,2,3,5,61,2,3,5,6.

(□+□−□)×□÷□=4 (\square+\square-\square) \times \square \div \square=4

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

The operation is equivalent to

(□+□−□)×□=4× (\square+\square-\square) \times \square=4 \times

Therefore, the left side of the equality is a multiple of 4, so the only possibilities are:

(□+□−□)×□=4×□ or (□+□−□)×□=4×□ (\square+\square-\square) \times \square=4 \times \square \quad \text { or } \quad(\square+\square-\square) \times \square=4 \times \square

From this, we can conclude that:

(3+5−□)×□=4×□ or (6+5−□)×□=4×□ (\boxed{3}+5-\square) \times \square=4 \times \square \quad \text { or } \quad(6+5-\square) \times \square=4 \times \square

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.