Maths Olympiad Prep

Track / Stage 4 / 208 of 340 #468 of 1964

Problem 468

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

26. For a cube with edge length of mm cm, some of its faces are painted red, and then it is cut into small cubes with edge length of 1 cm. The ratio of the number of small cubes with at least one red face to the number of small cubes with no red surface is 13:1213: 12. What is the minimum value of mm at this time? \qquad

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

Official solution

answer: 5

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