Random Puzzles 

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747

Workings

Hint
Jesse is the oldest.

Answer
Morgan is 3 and has two teddies.
Pat is 1 and has one teddies.
Jesse is 4 and has three teddies.
Dale is 2 and has four teddies.

Workings

Hint
Find how many sheep Drew has first.

Answer
3.

Reasoning
If we denote Alex by A, Billie by B, Charlie by C, and Drew by D and number the clues.

If Alex had three more sheep, then he'd have one fewer sheep than Billie. Whereas Drew has the same number as the other three shepherds put together. If Charlie had three fewer sheep, he'd have exactly three times the number of Alex. If they were evenly distributed, they'd each have eleven sheep.
By (4):
   A + B + C + D = 44

And, by (2), these are shared equally between A + B + C and D.

So D = 22, and A + B + C = 22 (*)

By (1):
   A + 3 = B – 1
   A + 4 = B

By (3):
   C – 3 = 3A
   C     = 3A + 3

Substitute B and C in (*):

A + (A+4) + (3A+3) = 22
            5A + 7 = 22
                5A = 15
                 A = 3

And, B = 7, C = 12.

Double-Checking
A = 3, B = 7, C = 12, D = 22.

(1) 3 + 3 = 7 – 1
(2) 3 + 7 + 12 = 22
(3) 12 – 3 = 3 x 3
(4) 3 + 7 + 12 + 22 = 44, and 44 ÷ 4 = 11 each.

Workings

Hint
Read the question carefully.

Answer
56 cubic feet (= 4 x 7 x 2).

We usually ask how much earth there is in a hole, which of course there is none!