Problem 2 · 2012 Math Kangaroo
Easy
Counting & Probability
careful-counting
Barbara wrote the word MATHEMATIC on a piece of paper. She used the same colour for letters that are the same, and a different colour for letters that are different. How many different colours did she use?
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Answer: A — 7
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Hint 1 of 2
Write out the letters of MATHEMATIC and circle the ones that repeat.
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Hint 2 of 2
Count how many different letters appear, not how many letters there are.
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Approach: count the distinct letters
- MATHEMATIC uses the letters M, A, T, H, E, M, A, T, I, C.
- The repeats are the second M, the second A and the second T.
- The different letters are M, A, T, H, E, I, C — that is 7.
- So she used 7 colours.
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