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Problem 110

Combinatorics Difficulty 1.3 Multiple choice CEMC Pascal · Canada · 2023

A sign has 31 spaces on a single line.

The word RHOMBUS is written from left to right in 7 consecutive
spaces.

There is an equal number of empty spaces on each side of the word.

Counting from the left, in what space number should the letter R be
put?

Pick one

Official solution

Since the letters of RHOMBUS take up 7 of the 31 spaces on the
line, there are $31 - 7 = 24$ spaces
that are empty.

Since the numbers of empty spaces on each side of RHOMBUS are the same,
there are $24 \div 2 = 12$ empty
spaces on each side.

Therefore, the letter R is placed in space number $12 + 1 = 13$ , counting from the left.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.