The Presents Puzzle
A probability puzzle about search strategies

Charlie puts presents in boxes, labeled 1 to 100. Each second, Alice and Bob look in one box. Alice opens them in order (1, 2, 3, …), while Bob opens the odds first, then the evens (1, 3, 5, …, 2, 4, 6, …). Who is more likely to see all 26 presents first?

Alice (0/100)

0/26
1
2
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100
Opens in order: 1, 2, 3, 4, 5, ...

Bob (0/100)

0/26
1
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100
Opens odds first, then evens: 1, 3, 5, ..., 2, 4, 6, ...

💭 Think About It

At first glance, both strategies seem equivalent—they both check all 100 boxes eventually. But the order matters! Try running the simulation multiple times to see which strategy performs better on average. Can you explain why?

This simulation was inspired by this tweet by Daniel Litt, which in turn is a variation of this puzzle by Gil Kalai.