Track / Stage 4 / 219 of 340 #479 of 1964

Problem 479

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

Does there exist a four-digit natural number with distinct non-zero digits that has the following property: if this number is added to the same number written in reverse order, the result is divisible by $101$ ?

Your answer

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

Official solution

1. Answer. It exists.

For example, the number 1234 works. Indeed, $1234+4321=5555=101 \cdot 55$ .

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