Maths Olympiad Prep

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Problem 909

AMC 12 late, AIME early
Combinatorics Difficulty 4.0 Find the answer BMO Round 1 · United Kingdom · 2019

A list of five two-digit positive integers is written in increasing order on a blackboard. Each of the five integers is a multiple of 33, and each digit 0,1,2,3,4,5,6,7,8,90,1,2,3,4,5,6,7,8,9 appears exactly once on the blackboard. In how many ways can this be done? Note that a two-digit number cannot begin with the digit 00.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.