Maths Olympiad Prep

Track / Stage 4 / 72 of 340 #332 of 1964

Problem 332

AMC 12 late, AIME early
Combinatorics Difficulty 4.7 Find the answer

157. Secret Code. Two conspirators had a secret code. Sometimes their correspondence contained simple arithmetic operations that looked completely innocent. However, in the code, each of the ten digits represented its own letter of the alphabet. Once, a sum was encountered which, after substituting the corresponding letters for the digits, took the form

FLYFORYOURLIFE \begin{gathered} F L Y \\ F O R \\ Y O U R \\ \hline L I F E^{* *} \end{gathered}

It would be interesting to restore this sum, knowing that II and OO represent the digits 1 and 0, respectively.

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

157.

598

+507 +507

80479152 \begin{array}{r} 8047 \\ \hline 9152 \end{array}

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