Problem 12 · 2018 Math Kangaroo
Medium
Counting & Probability
careful-counting
You make two-digit numbers using the digits 2, 0, 1 and 8. Each number must be bigger than 10 and smaller than 25, and made of two different digits. How many different numbers do you get?
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Answer: A — 4
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Hint 1 of 3
The number is between 10 and 25, so it must start with a 1 or a 2 — try each.
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Hint 2 of 3
For a number starting with 1, the other digit comes from 2, 0, 8 (a 1 would repeat).
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Hint 3 of 3
Write out every number you can make, then cross off any below 11 or 25 and up, and any with two equal digits.
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Approach: list every allowed number and count them
- The number is bigger than 10 and smaller than 25, so it starts with 1 or 2.
- Starting with 1, the other digit (from 2, 0, 8) gives 12, 10, 18 — but 10 is not bigger than 10, so keep 12 and 18.
- Starting with 2, staying under 25, gives 20 and 21. All together: 12, 18, 20, 21, which is 4 numbers.
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