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Problem 551

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

(12 points) The six-digit number $20 \square 15 \square$ is divisible by 72. What is this six-digit number?

Your answer

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

Official solution

【Solution】Solution: If the six-digit number $20 \square 15 \square$ can be divided by 72, then the six-digit number $20 \square 15 \square$ can be divided by 8,

then 15 口 can be divided by 8,
so 口 $=2$ . Then the six-digit number $20 \square 15 \square$ can be divided by 9, so $2+0+$ 口 $+1+5+2=10+$ 口 can be divided by 9, so 口 $=8$ ,

so this six-digit number is 208152,
Answer: This six-digit number is 208152.

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