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.
Puzzle One
What number should be subtracted from 13/12 to get 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?
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?
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?
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Last month's solutions
Puzzle One
How many 3-digit numbers are divisible by 7?
Solution:
The largest 2-digit and 3-digit numbers divisible by 7 are:
98 = 14 x 7 and 994 = 142 x 7.
There are therefore, including zero, 15 1- and 2-digit numbers divisible by 7, and
143 1-, 2- and 3-digit numbers divisible by 7.
Thus, 143 – 15 = 128 3-digit numbers divisible by 7.
Puzzle Two
In a certain class, 60% of the students are female and 40% are male. If 80% of the females and 50% of the males get A grades, what percentage of the class gets an A?
Solution:
Suppose there are n students in the class. Then there are 0.60 x n females and 0.40 x n males in the class.
(0.80 x 0.60) x n = 0.48 x n females & (0.70 x 0.40) x n = 0.28 x n males get an A.
Therefore, (0.48 + 0.28) x n =.0.76 x n, or 76%, of the class get an A.
Puzzle Three
A certain number of persons are standing in a row. Jake is18th from the left end and Tiny is 23rd from the right end. If they interchange their positions, Tiny becomes 33rd from the right end. How many persons are in the row?
Solution:
 |
Therefore, the number of persons in the row = 18 + 33 – 1 (Jake included twice) = 50
Puzzle Four
A ship is sailing north at a speed of 20 km/hour. A second ship directly south of this is sailing east at a speed of 15 km/h. How fast are they travelling apart?
Solution:
Each hour the ships will have increased their South North separation by 20 km and their West East separation by 15 km.
Using Pythagorean Theorem for right triangles (a² + b² = c²):
Thus, the ships will have an increased separation of
√(202 + 152) = √625 = 25 km.
The ships are, therefore, travelling apart at a rate of 25 km/h