Maths Olympiad Prep

Track / Stage 4 / 293 of 340 #553 of 1964

Problem 553

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

The blackboard has the following 9 numbers written on it. Each time, the teacher arbitrarily erases two numbers, and writes their sum on the blackboard. When only one number remains on the blackboard, this number is \qquad.

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

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Official solution

answer: 90

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.