2025 AMC 8 Problem 15
Attempt Problem 15 of the 2025 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
Kei draws a -by- grid. He colors of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let and equal the least and greatest possible number of gold-on-gold pairs, respectively. What is the value of
Answer: C
Small hint:
The fold makes overlapping pairs
Big hint:
To minimize double-gold pairs, spread gold squares among pairs first
Video solution:
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Written solution:
The number of gold squares is The total squares overlap as pairs.
To minimize the number of pairs with two gold squares, the gold squares should first be spread out across all pairs. That uses up of them. The remaining gold squares double-up and create a total of gold-on-gold pairs.
To maximize the number of pairs with two gold squares, the gold squares should first be paired up as much as possible. That can be done to create pairs, with gold square left over, because is with a remainder of
The answer is which is choice C.
Problem 15 in other years
- 1985 AMC 8
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