Random Puzzles 

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 + N
             —
             4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.

Workings

Hint
Try working backwards.

Answer
335 strawberries.

Reasoning
Working backwards …

I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.

I ate 6 myself, so I had 108 before I ate those.

I had 108 strawberries, so I had 162 before giving Billie one third.

I ate 3 myself, so I had 165 before I ate those.

I had 165 strawberries, so I had 330 before giving Alex one half.

Ate 5 myself, so I had 335 before I ate those.

Therefore, I started with 335 strawberries.

Double-Checking
I started with 335.

I ate 5, leaving 330.

I gave Alex half (165), leaving 165.

I ate 3, leaving 162.

I gave Billie one third (54), leaving 108.

I ate 6, leaving 102.

I gave Charlie two thirds (68), leaving 34.

Workings

Hint
One of the winners is called Jack.

Answer
DEEFIJOORST      = JODIE FOSTER
EEELMPRRSTY      = MERYL STREEP
ABEIJLORRSTU     = JULIA ROBERTS
AABEEHHIKNNPRRTU = KATHARINE HEPBURN
CEEEGGLNOOORY    = GEORGE CLOONEY
ACCHIJKLNNOOS    = JACK NICHOLSON
BDEEINOORRRT     = ROBERT DE NIRO
AACCEEHIILMN     = MICHAEL CAINE

Workings

Hint
Think of an alternative alphabet.

Answer
N.

From epsiloN, last letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu.