Problem 17 · 2015 Math Kangaroo
Medium
Spatial & Visual Reasoning
balance-scale
Four objects a, b, c, d are placed on a double balance as shown. Then two of the objects are exchanged, which results in the change of position of the balance as shown. Which two objects were exchanged?
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Answer: D — a and d
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Hint 1 of 2
Track which pan tips in each balance before and after the swap.
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Hint 2 of 2
Test swaps of two objects and see which single exchange flips the balances to the shown new state.
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Approach: test each possible exchange against the new tilt
- The two balances pin down the relative weights of a, b, c, d before the swap.
- After exchanging two objects, the balance tilts change to the pictured arrangement.
- Only swapping a and d reproduces the new positions.
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