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Mathematical Puzzles


Difficulty: MediumPuzzle 21

Puzzle IconMy bath has two taps and a plug hole.

The cold tap on its own fills the bath in 18 minutes, the hot one in 15 minutes.

The plug hole can drain the bath in 10 minutes with the taps off.

How long will the bath take to fill if I leave both taps on with the plug left out?

[Ref: ZCSZ] Copyrighted

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Difficulty: MediumPuzzle 22

Puzzle IconDuring a recent BrainBashers thinking contest, the total number of points scored by the first six players was 103 and every score was above zero.

The first player scored half the points of the second player, who in turn scored 6 points fewer than the third player.

The third player in turn scored two thirds the points of the fourth player.

The fifth player managed to score the same number of points as the difference between the first and fourth player's points.

Finally, the sixth player scored 14 fewer than the fifth player.

Can you determine how many points the sixth player managed to score?

[Ref: ZRIL] © Kevin Stone

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Difficulty: MediumPuzzle 23

Puzzle IconDuring the recent BrainBashers football competition, 5 schools were competing.

Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost.

Here are the final points after all of the matches:

Longton     6
Fenton      5
Blurton     4
Hulton      2

Fulton      ==?==

How many points did Fulton end the season with?

[Ref: ZBIL] © Kevin Stone

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Difficulty: MediumPuzzle 24

The surface area of a spherical balloon measured in square inches is the same as its volume, measured in cubic inches. What is the diameter of the balloon?

[Ref: ZEZW]

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