Question

Assume that we have six positive real numbers whose sum is 150. Prove that there exist two of them whose difference is less than 10.

score 5.3k · Answer 1 · 2018-04-25 04:20:37

Assume that we have six positive real numbers whose sum is 150. Prove that there exist two of them whose difference is less than 10.

score 2.5k · Answer 2 · 2018-04-29 14:34:52

2.5k

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The Pigeonhole Principle

Published on 29 Apr 2018 - 14:34

score 325 · Answer 3 · 2018-04-29 22:13:32

325

Views

Prove that for any set of $n$ integers, there exists a nonempty subset whose elements sum to a multiple of $n$.

Published on 29 Apr 2018 - 22:13

score 79 · Answer 4 · 2018-05-01 10:37:08

79

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Subset of finite set having the same cardinality

Published on 01 May 2018 - 10:37

score 194 · Answer 5 · 2018-05-01 19:52:19

194

Views

Prove that any $6$- subset of integers $\{1...14\}$ is always the union of two distinct subsets of equal sum

Published on 01 May 2018 - 19:52

score 550 · Answer 6 · 2018-05-03 05:46:53

550

Views

British Maths Olympiad (BMO) 2004 Round 1 Question 3 Proof with pigeon hole principle?

Published on 03 May 2018 - 5:46

score 1.2k · Answer 7 · 2018-05-06 02:07:02

1.2k

Views

There are $12$ signs of zodiac. How many people are needed to guarantee that at least $6$ of these people have the same sign?

Published on 06 May 2018 - 2:07

score 13.9k · Answer 8 · 2018-05-06 03:12:55

13.9k

Views

Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n

Published on 06 May 2018 - 3:12

score 957 · Answer 9 · 2018-05-06 17:48:00

957

Views

Pigeonhole Principle(Numerical Example)

Published on 06 May 2018 - 17:48

score 512 · Answer 10 · 2018-05-09 17:34:59

512

Views

How Many Times Would I Need To Draw a Sock to Get a Matching Pair?

Published on 09 May 2018 - 17:34

score 779 · Answer 11 · 2018-05-11 11:06:46

779

Views

Finding equal partial sum given two $N$-tuples of natural numbers

Published on 11 May 2018 - 11:06

score 71 · Answer 12 · 2018-05-12 04:41:13

71

Views

Property of natural numbers using pigeonhole principle

Published on 12 May 2018 - 4:41

score 164 · Answer 13 · 2018-05-12 18:15:09

164

Views

Dirichlet box principle

Published on 12 May 2018 - 18:15

score 144 · Answer 14 · 2018-05-15 06:06:11

144

Views

maximum size of a subset with no two elements $x,y$ such that $x-y $ divides $x+y$

Published on 15 May 2018 - 6:06

score 33 · Answer 15 · 2018-05-17 16:12:54

33

Views

pigeon hole sequence problem

Published on 17 May 2018 - 16:12

List Question

Assume that we have six positive real numbers whose sum is 150. Prove that there exist two of them whose difference is less than 10.

The Pigeonhole Principle

Prove that for any set of $n$ integers, there exists a nonempty subset whose elements sum to a multiple of $n$.

Subset of finite set having the same cardinality

Prove that any $6$- subset of integers $\{1...14\}$ is always the union of two distinct subsets of equal sum

British Maths Olympiad (BMO) 2004 Round 1 Question 3 Proof with pigeon hole principle?

There are $12$ signs of zodiac. How many people are needed to guarantee that at least $6$ of these people have the same sign?

Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n

Pigeonhole Principle(Numerical Example)

How Many Times Would I Need To Draw a Sock to Get a Matching Pair?

Finding equal partial sum given two $N$-tuples of natural numbers

Property of natural numbers using pigeonhole principle

Dirichlet box principle

maximum size of a subset with no two elements $x,y$ such that $x-y $ divides $x+y$

pigeon hole sequence problem

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