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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

## ARITH-maze puzzle

 Go to START and proceed through this numeric maze, following instructions until you get to the FINISH box. What number did you finish with?

## Feedback

There are more than one way of doing these puzzles and may well be more than one answer.  Please let me and others know what alternatives you find by commenting below.  We also welcome general comments on the subject and any feedback you'd like to give.

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## Puzzle One

What number should be subtracted from 13/12 to get 12/13?

Solution:

Let n = number needed
(13/12 – n) = 12/13
12(13/12 – n) = 12(12/13)
13 – 12n = 144/13
-12n = 144/13 – 13(13/13) =
– 12n =144/13 – 169/13) = -25/13
n = 25 / (13*12)
n = 25/156
Checking: (13/12) – (25/156) = (169/156) – (25/156) = 144/156 =12/13

## Puzzle Two

Container A holds 5 times as much milk as Container B. After 1.25 litres of milk from Container A is poured into Container B, both containers have the same amount of milk. How much milk did each container hold at first?

Solution:

Let container B contain x litres of milk
Then, container A contains 5x litres of milk
After 1.25 litres of milk from container A is poured into container B, both containers have the same amount of milk or
(5x – 1.25) = (x + 1.25); 4x = 2.5; x = 0.625 litres

Therefore at first, container B had 0.625 litres of milk and
container A had 0.625 x 5 = 3.125 litres of milk.

## Puzzle Three

There are some people on a boat. 48 get off the boat at the first stop. 62 people get on the second stop and half that is on the boat got off at the third stop. Now there are 73 people on the boat. How many people were on the boat prior to the first stop?

Solution:

Let x = number of people on the boat prior to its 1st stop.
Then, (on prior to 1st stop) – (off after 1st stop) + (on at 2nd stop) – (off after 3rd stop) = (on after 3rd stop)
Therefore, x – 48 + 62 – ½ (x – 48 + 62) = 73
x – 48 + 62 – ½ x + 24 – 31 = 73
½ x = 73 + 48 – 62 – 24 + 31 = 66
x = 66 * 2 = 132 people on the boat prior to the first stop.

## Puzzle Four

King Tut died 120 years after King Eros was born. Their combined ages when they died was 100 years. King Eros died in the year 40 B.C. In what year was King Tut born?