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? |
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Last month's solutions
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?
Answer:
King Tut was born in 20 B.C.
Solution:
There were 120 years between the birth of King Eros and the death of King Tut, but since their combined ages amounted to only 100 year, there must have been 20 years (120 – 100) when King Tut did not exist. This would be a period between the death of King Eros, 40 B.C., and the birth of King Tut, year 20 B.C.