Problem 10 · 2024 Math Kangaroo
Medium
Counting & Probability
careful-countingsum-constraint
The numbers 1, 2, 3, 4 and 5 are written on the board. Ali chooses 2 of them and adds them together. How many different results are possible?
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Answer: C — 7
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Hint 1 of 3
The very smallest answer comes from adding the two smallest numbers, 1 and 2.
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Hint 2 of 3
The very biggest answer comes from adding the two biggest numbers, 4 and 5.
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Hint 3 of 3
Once you know the smallest and biggest answers, count the numbers in between — but only count each answer once.
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Approach: find the smallest and biggest sum, then count in between
- The smallest sum is 1 + 2 = 3, and the biggest sum is 4 + 5 = 9.
- Every number from 3 up to 9 can be made, and none is skipped: 3, 4, 5, 6, 7, 8, 9.
- Counting those answers gives 7 different results.
Mark:
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