Question

Which axioms of the foundation of natural numbers are used in the proof of the pigeonhole principle?

score 785 · Answer 1 · 2026-03-26 21:10:32

785

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Which axioms of the foundation of natural numbers are used in the proof of the pigeonhole principle?

Published on 26 Mar 2026 - 21:10

score 912 · Answer 2 · 2026-03-28 15:20:17

912

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Given 5 Points on the surface of a sphere. 4 of them lie on the same hemisphere

Published on 28 Mar 2026 - 15:20

score 6.3k · Answer 3 · 2016-10-26 09:17:41

6.3k

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Suppose that 21 girls and 21 boys enter a math contest, Show that there is a question that was solved by at least three girls and at least three boys.

Published on 26 Oct 2016 - 9:17

score 552 · Answer 4 · 2016-10-29 12:51:01

552

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A Problem in Pigeonhole Principles.

Published on 29 Oct 2016 - 12:51

score 1k · Answer 5 · 2016-10-31 08:12:32

1k

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If $A\subset\{1,11,21,31,...,541,551\}$ such that $\forall x,y\in A: x+y\ne 552$, then $|A|\le28$

Published on 31 Oct 2016 - 8:12

score 1.8k · Answer 6 · 2016-10-31 20:11:33

1.8k

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Finding two integers to equal 26

Published on 31 Oct 2016 - 20:11

score 12.2k · Answer 7 · 2016-11-04 10:54:24

12.2k

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Prove that for any set of 5 integers, there is at least one subset of 3 integers whose sum is divisible by 3

Published on 04 Nov 2016 - 10:54

score 451 · Answer 8 · 2016-11-04 21:24:13

451

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Show that every subset with 6 elements of {1,2,3,4, ..., 9} contains 2 elements with sum 10.

Published on 05 Nov 2016 - 22:09

score 564 · Answer 10 · 2016-11-10 07:39:17

564

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Prove that there are at least 3 similar digital sums among 35 integers

Published on 10 Nov 2016 - 7:39

score 1.1k · Answer 11 · 2016-11-12 13:56:28

1.1k

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Pigeonhole: Committee of senators who hate one another

Published on 12 Nov 2016 - 13:56

score 2.5k · Answer 12 · 2016-11-17 01:12:43

2.5k

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How many socks take from the shelf to ensure that at least 2 of them have the same colour?

Published on 17 Nov 2016 - 1:12

score 1.6k · Answer 13 · 2016-11-17 04:27:35

1.6k

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pigeonhole principle clarification

Published on 17 Nov 2016 - 4:27

score 71 · Answer 14 · 2026-03-26 12:53:34

71

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Prove that in every coloration of the following graph, there exists one red or/and one yellow triangle.

Published on 26 Mar 2026 - 12:53

score 247 · Answer 15 · 2016-11-22 00:18:11

247

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How can you prove that two random integers out of 52 are a multiple of 100?

Published on 22 Nov 2016 - 0:18

List Question

Which axioms of the foundation of natural numbers are used in the proof of the pigeonhole principle?

Given 5 Points on the surface of a sphere. 4 of them lie on the same hemisphere

Suppose that 21 girls and 21 boys enter a math contest, Show that there is a question that was solved by at least three girls and at least three boys.

A Problem in Pigeonhole Principles.

If $A\subset\{1,11,21,31,...,541,551\}$ such that $\forall x,y\in A: x+y\ne 552$, then $|A|\le28$

Finding two integers to equal 26

Prove that for any set of 5 integers, there is at least one subset of 3 integers whose sum is divisible by 3

More advanced pigeonhole principle problem, uncertain how answer was derived

Show that every subset with 6 elements of {1,2,3,4, ..., 9} contains 2 elements with sum 10.

Prove that there are at least 3 similar digital sums among 35 integers

Pigeonhole: Committee of senators who hate one another

How many socks take from the shelf to ensure that at least 2 of them have the same colour?

pigeonhole principle clarification

Prove that in every coloration of the following graph, there exists one red or/and one yellow triangle.

How can you prove that two random integers out of 52 are a multiple of 100?

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