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Mathematical Puzzles


Difficulty: HardPuzzle 1

The Miller next took the company aside and showed them nine sacks of flour that were standing as depicted in the sketch.

"Now, hearken, all and some," said he, "while that I do set ye the riddle of the nine sacks of flour.

And mark ye, my lords and masters, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof.

By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 196, which is of a truth the number shown by the sacks in the middle.

Yet it be not true that the other pair, 34, when so multiplied by its neighbour, 5, will also make 196.

Wherefore I do beg you, gentle sirs, so to place anew the nine sacks with as little trouble as possible that each pair when thus multiplied by its single neighbour shall make the number in the middle."

As the Miller has stipulated in effect that as few bags as possible shall be moved, there is only one answer to this puzzle, which everybody should be able to solve.

Puzzle Image

[Ref: ZYIT] The Miller's Puzzle. The Canterbury Puzzles And Other Curious Problems by Henry Ernest Dudeney (1907).

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Direct Link: www.brainbashers.com?ZYIT


Difficulty: EasyPuzzle 2

Puzzle IconA large fresh water reservoir has two types of drainage system. Small pipes and large pipes.

6 large pipes, on their own, can drain the reservoir in 12 hours.

6 small pipes, on their own, can drain the reservoir in 18 hours.

How long will 6 large pipes and 6 small pipes take to drain the reservoir?

[Ref: ZNEC] © Kevin Stone

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Direct Link: www.brainbashers.com?ZNEC


Difficulty: EasyPuzzle 3

Puzzle IconIn the local wood there are a number of trees. On these trees there are a number of birds.

The local game keeper knows that there are as many birds on each tree as there are trees in the wood.

He also knows that there are between 2000 and 2100 birds in total. How many trees are there in the wood?

[Ref: ZSQB] © Kevin Stone

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Direct Link: www.brainbashers.com?ZSQB


Difficulty: EasyPuzzle 4

Puzzle IconAt midnight at the start of Monday, January 1st, Professor Stone set two of his old fashioned clocks to the correct time.

One of his clocks gains one minute every hour and the other loses two minutes every hour.

1. When will the clocks next show the same time as each other?
2. When will the clocks both show the correct time?

[Ref: ZDJB] © Kevin Stone

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Direct Link: www.brainbashers.com?ZDJB

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