Pigeonhole Principle: Theory, Logic, and Applications Quiz

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| Questions: 15 | Updated: Dec 1, 2025
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1) The basic pigeonhole principle states that if objects are placed into boxes and , then:

Explanation

More objects than boxes forces at least one box to contain ≥2.

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About This Quiz
Pigeonhole Principle: Theory, Logic, And Applications Quiz - Quiz

Think you understand how the pigeonhole principle works behind the scenes? This quiz dives deeper into its logic, terminology, and the kinds of arguments it supports in graduate-level combinatorics. You’ll analyze objects placed into bins, residue classes, averages, collisions, and structural guarantees in mathematical systems. Along the way, you’ll work... see morewith modular arithmetic, hashing ideas, and nonconstructive proof strategies. By the end, you’ll see how this fundamental principle becomes a powerful tool for proving patterns, constraints, and impossibilities across a wide range of mathematical settings. see less

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2) The generalized pigeonhole principle says some box contains at least objects.

Explanation

It states some box has at least ⌈n/k⌉ objects.

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3) If 32 items are placed into 7 bins, the minimum number guaranteed in one bin is:

Explanation

⌈32/7⌉ = 5.

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4) A “pigeon” refers to:

Explanation

In the principle, pigeons = objects.

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5) A “pigeonhole” refers to:

Explanation

Pigeonholes = boxes/categories receiving objects.

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6) You can apply the pigeonhole principle to infinite sets without modification.

Explanation

The classical form assumes finite sets.

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7) If you place 10 integers into 3 residue classes modulo 3, at least one class contains at least:

Explanation

⌈10/3⌉ = 4.

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8) Which situations naturally use the pigeonhole principle?

Explanation

All involve more items than categories → forced repetition.

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9) If 20 people each pick a number from 1 to 15, then at least two people choose:

Explanation

20 > 15 → two must pick the same number.

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10) If you distribute items among boxes, then the average number per box is .

Explanation

Average = total objects ÷ total boxes.

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11) If 17 exam papers are placed into 4 folders, one folder has at least:

Explanation

⌈17/4⌉ = 5.

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12) The pigeonhole principle is often used to prove existence, not to construct specific examples.

Explanation

It is a non-constructive proof method.

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13) A collision in hashing terminology corresponds to:

Explanation

A collision occurs when multiple items hash to one location.

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14) Which statements characterize the pigeonhole principle?

Explanation

It forces duplication and applies to categorized outcomes.

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15) You choose 50 integers from the set . What must be true?

Explanation

45 remainder classes → 50 choices guarantee a repeat.

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The basic pigeonhole principle states that if objects are placed into...
The generalized pigeonhole principle says some box contains at least...
If 32 items are placed into 7 bins, the minimum number guaranteed in...
A “pigeon” refers to:
A “pigeonhole” refers to:
You can apply the pigeonhole principle to infinite sets without...
If you place 10 integers into 3 residue classes modulo 3, at least one...
Which situations naturally use the pigeonhole principle?
If 20 people each pick a number from 1 to 15, then at least two people...
If you distribute items among boxes, then the average number per box...
If 17 exam papers are placed into 4 folders, one folder has at least:
The pigeonhole principle is often used to prove existence, not to...
A collision in hashing terminology corresponds to:
Which statements characterize the pigeonhole principle?
You choose 50 integers from the set . What must be true?
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