- 1.
Let S ⊆ {1, 2, 3, …, 9} where |S| = 5. Prove that the sums of the elements in all the nonempty subsets of S can not all be distinct.
- 題型：問答題
- 難易度：尚未記錄
- 2.
- 題型：問答題
- 難易度：尚未記錄
- 3.
For any integer n ≥ 24, show that n can be written as a sum of 5's and/or 7's.
- 題型：問答題
- 難易度：尚未記錄
- 4.
How many nonnegative integer solutions to the following equations: x1 + x2 + x3 + x4 + x5 = 23 and x1 + x2 = 10?
- 題型：問答題
- 難易度：尚未記錄
- 5.
A 5-star graph is an undirected graph G(V, E) where |V| = 5!. Each node is uniquely assigned a label x1x2x3x4x5 which is a permutation of {1, 2, 3, 4, 5}. Each node x1x2x3x4x5 is adjacent to node xi...x1 ...for 2 ≤ i ≤ 5. Determine whether the graph has an Euler circuit and/or a Hamiltonian cycle.
- 題型：問答題
- 難易度：尚未記錄