Mathematical Puzzles 

The Miller's Puzzle – 'The Canterbury Puzzles And Other Curious Problems' by Henry Ernest Dudeney (1907).

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, 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.

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

A local bird spotter knows that there are as many birds on each tree as there are trees in the wood, and that there are between 2000 and 2100 birds in total. How many trees are there in the wood?

Puzzle Copyright © Kevin Stone

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

One clock gains one minute every hour and the other loses two minutes every hour.

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

Puzzle Copyright © Kevin Stone

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Alex and Blake were rowing their canoe along the River Trent.

In the morning they managed to row upstream at an average speed of 2 miles per hour.

They then stopped for a spot of lunch and a nice rest.

In the afternoon, the pace was a little easier as they were now rowing downstream back to their starting point, and managed an average speed of 4 miles an hour.

The morning trip took them 3 hours longer than the afternoon.

How far did they row upstream?

Puzzle Copyright © Kevin Stone

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