Generalized Pigeonhole Principle — Harder Reasoning

  • Grade 12th
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| Questions: 10 | Updated: Nov 12, 2025
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1) What is the minimum number of people required to ensure at least 10 share a birthday day of the week?

Explanation

7(10−1)+1=647(10−1)+1 = 647(10−1)+1=64

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About This Quiz
Generalized Pigeonhole Principle Harder Reasoning - Quiz

Take pigeonhole reasoning to the next level! This quiz presents more complex problems where careful logic is required. Try this quiz to sharpen your skills in tackling non-obvious applications of the principle.

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2) How many marbles must be placed into 15 jars to guarantee one jar contains at least 12 marbles?

Explanation

15(12−1)+1=16615(12−1)+1 = 16615(12−1)+1=166

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3) If 121 items are placed in 12 boxes, at least how many must be in one box?

Explanation

⌈121/12⌉=⌈10.08...⌉=11\lceil 121/12 \rceil = \lceil 10.08...\rceil = 11⌈121/12⌉=⌈10.08...⌉=11

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4) If 500 objects are distributed into 37 boxes, what is the minimum in one box?

Explanation

⌈500/37⌉=⌈13.51⌉=14\lceil 500/37 \rceil = \lceil 13.51 \rceil = 14⌈500/37⌉=⌈13.51⌉=14

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5) What is the least number of cards to guarantee at least 6 of the same suit? (4 suits)

Explanation

4(6−1)+1=234(6−1)+1 = 234(6−1)+1=23

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6) A competition has 250 participants divided among 11 teams. Minimum guaranteed in one team?

Explanation

⌈250/11⌉=⌈22.72...⌉=25\lceil 250/11 \rceil = \lceil 22.72... \rceil = 25⌈250/11⌉=⌈22.72...⌉=25

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7) How many candies must be distributed among 20 kids to guarantee one kid gets at least 8 candies?

Explanation

20(8−1)+1=14120(8−1)+1 = 14120(8−1)+1=141

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8) If 333 beads are placed into 17 containers, the minimum beads in one container is

Explanation

⌈333/17⌉=⌈19.58...⌉=20\lceil 333/17 \rceil = \lceil 19.58...\rceil = 20⌈333/17⌉=⌈19.58...⌉=20

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9) How many people are needed to ensure at least 15 share a birth month?

Explanation

12(15−1)+1=16912(15−1)+1 = 16912(15−1)+1=169

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10) If 75 objects are placed into 8 boxes, the minimum in one box is

Explanation

⌈75/8⌉=⌈9.375⌉=10\lceil 75/8 \rceil = \lceil 9.375 \rceil = 10⌈75/8⌉=⌈9.375⌉=10

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What is the minimum number of people required to ensure at least 10...
How many marbles must be placed into 15 jars to guarantee one jar...
If 121 items are placed in 12 boxes, at least how many must be in one...
If 500 objects are distributed into 37 boxes, what is the minimum in...
What is the least number of cards to guarantee at least 6 of the same...
A competition has 250 participants divided among 11 teams. Minimum...
How many candies must be distributed among 20 kids to guarantee one...
If 333 beads are placed into 17 containers, the minimum beads in one...
How many people are needed to ensure at least 15 share a birth month?
If 75 objects are placed into 8 boxes, the minimum in one box is
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