🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2012 Math Kangaroo

Problem 2

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?

Show answer
Answer: A — 7
Show hints
Hint 1 of 2
Write out the letters of MATHEMATIC and circle the ones that repeat.
Still stuck? Show hint 2 →
Hint 2 of 2
Count how many different letters appear, not how many letters there are.
Show solution
Approach: count the distinct letters
  1. MATHEMATIC uses the letters M, A, T, H, E, M, A, T, I, C.
  2. The repeats are the second M, the second A and the second T.
  3. The different letters are M, A, T, H, E, I, C — that is 7.
  4. So she used 7 colours.
Mark: · log in to save