Problem 12 · Extreme cases · 4 points
Made by AI and not reviewed by a real person.
Pip puts 15 pebbles into four pockets. Each pocket has a different number of pebbles, no pocket is empty, and one pocket has exactly 4. What is the most pebbles one pocket can hold?
- 7
- 6
- 9
- 10
- 8
Show a hint
- To make one pocket hold the most, put as few as possible in the others.
Show the answer and solution
Answer: E — 8
One pocket has 4 pebbles. The two smallest other pockets can have 1 and 2, leaving 15 − 4 − 1 − 2 = 8 for the last pocket. The numbers 1, 2, 4, and 8 are all different, so 8 works. A tempting answer is 9, from 1, 2, 3, and 9—but then no pocket has 4.