Generalized Pigeonhole Principle — Basic Applications

  • Grade 11th
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| Questions: 10 | Updated: Nov 12, 2025
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1) If 25 objects are placed into 6 boxes, what is the minimum number of objects guaranteed in one box?

Explanation

⌈25/6⌉=⌈4.166...⌉=5\lceil 25/6 \rceil = \lceil 4.166...\rceil = 5⌈25/6⌉=⌈4.166...⌉=5

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About This Quiz
Generalized Pigeonhole Principle Basic Applications - Quiz

The pigeonhole principle is simple yet powerful. In this quiz, you’ll practice its generalized form in straightforward problems, building an intuition for how it applies to counting. Try this quiz to uncover hidden patterns in sets and groups.

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2) If 100 marbles are placed into 9 jars, the minimum number in one jar is

Explanation

⌈100/9⌉=⌈11.11...⌉=12\lceil 100/9 \rceil = \lceil 11.11... \rceil = 12⌈100/9⌉=⌈11.11...⌉=12

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3) How many people must be in a room to guarantee at least 9 share a birthday month?

Explanation

n=12(9−1)+1=97n = 12(9−1)+1 = 97n=12(9−1)+1=97

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4) If 90 papers are placed in 11 folders, minimum in one folder is

Explanation

⌈90/11⌉=⌈8.18...⌉=9\lceil 90/11 \rceil = \lceil 8.18...\rceil = 9⌈90/11⌉=⌈8.18...⌉=9

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5) If 50 pencils are distributed among 8 drawers, what is the least number guaranteed in one drawer?

Explanation

⌈50/8⌉=⌈6.25⌉=7\lceil 50/8 \rceil = \lceil 6.25 \rceil = 7⌈50/8⌉=⌈6.25⌉=7

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6) What is the minimum number of students needed to guarantee at least 5 students are in the same group, if there are 7 groups?

Explanation

We need nnn such that ⌈n/7⌉=5\lceil n/7 \rceil = 5⌈n/7⌉=5 → n=7×(5−1)+1=29n = 7×(5−1)+1 = 29n=7×(5−1)+1=29

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7) How many socks must you pick from a drawer containing 4 colors to guarantee at least 6 of the same color?

Explanation

Use n=k(m−1)+1=4(6−1)+1=21n = k(m-1)+1 = 4(6−1)+1 = 21n=k(m−1)+1=4(6−1)+1=21

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8) 73 balls are distributed among 12 bins. Minimum balls in one bin?

Explanation

⌈73/12⌉=⌈6.08...⌉=7\lceil 73/12 \rceil = \lceil 6.08... \rceil = 7⌈73/12⌉=⌈6.08...⌉=7

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9) For 15 objects and 4 boxes, what is the minimum number guaranteed in one box?

Explanation

⌈15/4⌉=4\lceil 15/4 \rceil = 4⌈15/4⌉=4

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10) For 37 objects and 5 boxes, what’s the minimum guaranteed in one box?

Explanation

⌈37/5⌉=⌈7.4⌉=8\lceil 37/5 \rceil = \lceil 7.4 \rceil = 8⌈37/5⌉=⌈7.4⌉=8

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If 25 objects are placed into 6 boxes, what is the minimum number of...
If 100 marbles are placed into 9 jars, the minimum number in one jar...
How many people must be in a room to guarantee at least 9 share a...
If 90 papers are placed in 11 folders, minimum in one folder is
If 50 pencils are distributed among 8 drawers, what is the least...
What is the minimum number of students needed to guarantee at least 5...
How many socks must you pick from a drawer containing 4 colors to...
73 balls are distributed among 12 bins. Minimum balls in one bin?
For 15 objects and 4 boxes, what is the minimum number guaranteed in...
For 37 objects and 5 boxes, what’s the minimum guaranteed in one...
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