Puzzle 1

Last week, I travelled from London to Stoke. On the first day I travelled one half of the distance. On day two, I travelled one third of the remaining distance. On day three, I travelled three quarters of the remaining distance. Yesterday I travelled one half of the remaining distance. I now have 5 miles left to travel. How far is it from Stoke to London in total?

 [Ref: ZRBH] © Kevin Stone [Protected Puzzle]

Hint: It might be easier to work backwards.

Answer: 120 miles.

On the first day I travelled 60 miles, leaving 60 miles. On day two I travelled 20 miles, leaving 40 miles On day three I travelled 30 miles, leaving 10 miles. Yesterday I travelled 5 miles, leaving 5 miles. QED.

Puzzle 2

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.

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

Hint: The two left numbers multiplied, or the right two numbers, should create the central number.

Answer: The way to arrange the sacks of flour is as follows: 2, 78, 156, 39, 4. Here each pair when multiplied by its single neighbour makes the number in the middle, and only five of the sacks need be moved.

There are just three other ways in which they might have been arranged (4, 39, 156, 78, 2; or 3, 58, 174, 29, 6; or 6, 29, 174, 58, 3), but they all require the moving of seven sacks.

Puzzle 3

Exactly how many minutes is it before seven o'clock, if 40 minutes ago it was three times as many minutes past two o'clock?

 [Ref: ZNNB] © Kevin Stone [Protected Puzzle]

Hint: How many minutes are there between 2:00 and 7:00?

Answer: 65 minutes.

There are 300 minutes between 2:00 and 7:00. We can ignore the "40 minutes ago" for a little while and share the remaining 260 minutes in the ratio 3:1, which is 195:65. Which means the 5 hours between 2:00 and 7:00 are made of up 195 minutes + 40 minutes + 65 minutes. Which means it is currently 65 minutes before 7:00. So it is now 5:55 (65 minutes before 7:00).

To double check, 40 minutes ago it was 5:15 - which is 195 minutes after 2:00, as required (as 65 x 3 = 195).

Puzzle 4

You are given a 10x10x10 cube composed of one thousand 1x1x1 "mini-cubes" glued together. If the outer most layer falls off, how many "mini-cubes" would have fallen off?

 [Ref: ZVPY]

Hint: Think about one face at a time.

Answer: 488.

You started with 10x10x10 = 1000 cubes. The outer layer falling off will leave you with 8x8x8 = 512 cubes, which means 488 cubes have fallen off.

Puzzle 5

How quickly can you find the answer to:

5  x  4  x  3  x  ...  x  -3  x  -4  x  -5