Problem 12 · 2021 Math Kangaroo
Medium
Arithmetic & Operations
work-backwardcareful-counting
The 5 balls shown begin to move at the same time in the directions of their arrows. When two balls going in opposite directions collide, the bigger ball swallows the smaller one and grows by the smaller ball's value, then keeps moving in its own direction (see the worked example). What is the final result of the collisions of the 5 balls?
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Answer: C
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Hint 1 of 2
When two balls bump head-on, the bigger one eats the smaller one and grows by its number, still going the same way.
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Hint 2 of 2
No ball ever disappears, so the final ball's number is just every ball's number added together — you only need its direction too.
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Approach: all the balls merge into one, so add the values and find the direction
- Nothing is ever lost in a collision, so the one ball left at the end is worth 10 + 9 + 3 + 7 + 20 = 49.
- Following the bumps shows the big left-going 20 keeps winning the head-on hits, so the surviving ball moves left.
- Matching '49 moving left' to the pictures gives option C.
- So the result is a ball worth 49 moving left (C).
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