Competition problem — Number theory

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Number theory Difficulty 4.9 AIME Find the answer

25. Seven people have seven cats; each cat eats seven mice, each mouse eats seven ears of barley, and from each ear can grow seven measures of grain. What are the numbers in this series and what is their sum? (The problem is reconstructed according to Rodet.)

## Problems from the Akhmim Papyrus.

Your answer

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

Solution

25. $7,49,343,2401,16807$ , sum 19607.

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