Maths Olympiad Prep

Track / Stage 5 / 14 of 400 #614 of 1964

Problem 614

AIME late
Combinatorics Difficulty 5.0 Find the answer

69. Fill the 12 natural numbers from 112211 \sim 22 into the small circles in the figure, each number must be used, and the sum of the four numbers on each side must be equal. The difference between the minimum and maximum value of this sum is \qquad .

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

Official solution

Answer: 8

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