Random Puzzles 

Workings

Hint
Who was going to St Ives?

Answer
One.

Reasoning
Only I was going to St Ives.

This is a very old puzzle, and appeared in a manuscript dated around 1730. It is thought to refer to a town in Cornwall, UK.

If we were to count everyone and everything, including all of the kits, cats, sacks and wives, we would have:
Me    = 1
Man   = 1
Wifes = 7
Sacks = 7 x 7 = 49
Cats  = 7 x 7 x 7 = 343
Kits  = 7 x 7 x 7 x 7 = 2401

Total = 1 + 1 + 7 + 49 + 343 + 2401 = 2,802.

Workings

Hint
The answer isn't very large at all.

Answer
There are four boys and six girls in the family.

If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.

And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
    2(b − 1) = g       [1]
       g − 1 = b + 1   [2]

Using [1] in [2] gives:

2(b − 1) − 1 = b + 1

Expanding the bracket gives:

  2b − 2 − 1 = b + 1

Simplifying the left hand side gives:

     2b − 3  = b + 1

Add 3 to each side gives:

          2b = b + 4

Subtract b from both sides gives:

           b = 4

Using b = 4 in [1] gives:

    2(4 − 1) = g

           6 = g

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
The word begins with the letter A.

Answer
Ask.

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