Maths Olympiad Prep

Track / Stage 4 / 320 of 340 #580 of 1964

Problem 580

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer

59. An electronic watch uses 5 two-digit numbers (including two-digit numbers with a leading 0) to indicate time and date, such as 15:23:45/06/18 representing June 18, 15:23:45. There are some special moments when all ten digits on the electronic watch are different. Among these special moments, the maximum sum of the 5 two-digit numbers on the electronic watch is \qquad .

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

Official solution

answer: 153

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