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Problem 296

Algebra Difficulty 1.8 Find the answer CEMC Pascal

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 RR be put?

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

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Official solution

Since the letters of RHOMBUS take up 7 of the 31 spaces on the line, there are 317=2431-7=24 spaces that are empty. Since the numbers of empty spaces on each side of RHOMBUS are the same, there are 24÷2=1224 \div 2=12 empty spaces on each side. Therefore, the letter R is placed in space number 12+1=1312+1=13, counting from the left.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.