Brain Teasers and Puzzles 

Workings

Hint
This is a simple substitution cipher.

Answer
50.

This puzzle is a simple test to see how easy a ROT13 part encrypted puzzle can be. Every other letter has been converted to ROT13 and the other letters are left as they were. But, you may ask, what is the puzzle? Well, how many words are in this puzzle!

ROT13 replaces each character with the one 13 places away.
A = N, B = O, C = P, D = Q, E = R, F = S, G = T, H = U, I = V, J = W, K = X, L = Y, M = Z, N = A, O = B, P = C, Q = D, R = E, S = F, T = G, U = H, V = I, W = J, X = K, Y = L, Z = M.

Workings

Hint
This question involves the months of the year in some way.

Answer
4 3 1.

Reasoning
This is the sequence of the length of the name of the month, and the number of days in that month.

7 3 1 = January, which has 7 letters, and 31 days.

8 2 8 = February, which has 8 letters, and 28 days.

5 3 1 = March, which has 5 letters, and 31 days.

5 3 0 = April, which has 5 letters, and 30 days.

3 3 1 = May, which has 3 letters, and 31 days.

4 3 0 = June, which has 4 letters, and 30 days.

Which means the next three digits are:

4 3 1 = July, which has 4 letters, and 31 days.

Workings

Hint
Can you see 1, 2, 3, …?

Answer
46.

Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1  1   (1 x 1 = 1,  reversed is 1)
2  4   (2 x 2 = 4,  reversed is 4)
3  9   (3 x 3 = 9,  reversed is 9)
4  61  (4 x 4 = 16, reversed is 61)
5  52  (5 x 5 = 25, reversed is 52)
6  63  (6 x 6 = 36, reversed is 63)
7  94  (7 x 7 = 49, reversed is 94)
   so we require:
8  46  (8 x 8 = 64, reversed is 46)

Workings

Hint
How many hands did the first person shake?

Answer
190.

The first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc:

19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 190