Random Puzzles 

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.

Workings

Hint
Try a random number of over 50s to see what happens.

Answer
20,064 apples.

Reasoning
It doesn't matter how old the people are.

As only ³/₄ of the over 50s claimed 16 apples, this averages out to 12 apples each.

Similarly, only ¹/₈ of the under 50s claimed 96 apples, this again averages out to be 12 apples each.

Therefore, the total number of apples was 1,672 x 12 = 20,064.

Workings

Hints
The first letters of the words are: F, H, A, B, C, R, P, K, Z, B.

Answers
fox horse antelope buffalo camel reindeer panther koala zebra badger

Workings

Hint
Start by labelling the number as ABCDE.

Answer
24,976.

Reasoning
We can start by labelling the digits as ABCDE.

We know that:

(i)  B = 2 x A

and:

     E = A + B

And using (i) we get:

     E = A + (2 x A)
(ii) E = 3 x A

If A = 1, this isn't allowed (as there are no 1's in the puzzle).

If A = 2, then B = 4, and E = 6.

If A = 3, then B = 6, and E = 9, but this isn't allowed (as C has to be the largest digit).

So, A = 2, B = 4, E = 6, and we now have to find C and D.

We also know that:

D = (A + B + C + D + E) ÷ 4

And using (i) and (ii) we get:

D = [A + (2 x A) + C + D + (3 x A)] ÷ 4

so:

3 x D = (6 x A) + C

so:

(iii) D = [(6 x A) + C] ÷ 3

C can only be 7, 8 or 9 (as it's the largest digit, and we've already found 6) and (iii) tells us that it must be a multiple of 3, which means that C = 9. Leaving D = 7.

So the final number is: 24976.

Double-Checking
The answer is 24976.

The fourth digit is a quarter of the total of all of the digits.
   A + B + C + D + E = 2 + 4 + 9 + 7 + 6 = 28, and 28 ÷ 4 = 7.

The second digit is twice the first digit.
   4 = 2 x 2.

The third digit is the largest.
   9 is the largest digit.

The last digit is the sum of the first two digits.
   6 = 2 + 4.