Prove that in an disordered set of 50 numbers, you can always remove 42 numbers in a way that leaves an ordered set of 8 numbers.
102740
What are some important applications of the Erdős-Szekeres Theorem?
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
86389
Combinatorial argument to prove the recurrence relation for number of derangements
1409
Proving that the given set has at most $2^{n-1}$ elements
47123
Suppose that a set has an odd number of elements. Explain why half of the subsets will have an odd number of elements
116251
Number of distinct total orders on a set
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
150647
How many $6$-lentgh increasing sequence are there from $1$ to $49$?
156242
As many even numbers as natural numbers.
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
103538
Partitions of $n$ into distinct odd and even parts proof
158882
Prove the existence of some weird family of sets
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
26569
Counting binary operations on a set with $n$ elements
92057
Prove that for every odd integer n, there is a group...
141298
Image of the set of natural numbers under any function is denumerable.
58103
number of permutations in which no two consecutive numbers are adjacent