Puzzle 5
Here we have a rectangular room, measuring 30 feet by 12 feet, and 12 feet high.
There is a spider in the middle of one of the end walls, 1 foot from the ceiling (A).
There is a fly in the middle of the opposite wall, 1 foot from the floor (B).
What is the shortest distance that the spider must crawl in order to reach the fly?
The Spider and the Fly, The Canterbury Puzzles, Henry Ernest Dudeney.
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Hint
Going down and across the floor isn't the only route.
Answer
40 feet.
Explanation Diagram
If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.
We can use Pythagoras' theorem (a2 + b2 = c2) to calculate the distances:
distance2 = horizontal2 + vertical2
distance = √(horizontal2 + vertical2)
Route #1
distance = 1 + 30 + 11 = 42 feet.
Route #2
horizontal = 6 + 30 + 6 = 42 feet.
vertical = 10 feet.
distance = √(422 + 102) ≈ 43.174 feet.
Route #3
horizontal = 1 + 30 + 6 = 37 feet.
vertical = 6 + 11 = 17 feet.
distance = √(372 + 172) ≈ 43.178 feet.
Route #4
horizontal = 1 + 30 + 1 = 32 feet.
vertical = 6 + 12 + 6 = 24 feet.
distance = √(322 + 242) = 40 feet.
Puzzle 7
What number comes next in this sequence:
986888
724864
143224
==??==
Puzzle Copyright © Kevin Stone
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Hint
The answer involves multiplication (for example, 9 x 8 = 72).
Answer
468.
Reasoning
If we split each line in the following way:
98 68 88
72 48 64
14 32 24
Each new line is generated by multiplying the digits two at a time and writing the result below.
For example, 9 x 8 = 72, so 72 appears directly below 98.
And 7 x 2 = 14, so 14 appears directly below 72.
Double-Checking
9 x 8 = 72, 7 x 2 = 14, 1 x 4 = 4.
6 x 8 = 48, 4 x 8 = 32, 3 x 2 = 6.
8 x 8 = 64, 6 x 4 = 24, 2 x 4 = 8.
Puzzle 8
A large freshwater 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?
Puzzle Copyright © Kevin Stone
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Hint
How many reservoirs can each drain in 36 hours?
Answer
7 hours and 12 minutes.
Reasoning
We can use a time that 12 hours and 18 hours both fit in to, in 36 hours:
6 large pipes can drain 3 reservoirs.
6 small pipes can drain 2 reservoirs.
Therefore, together, 6 large and 6 small pipes can drain 5 reservoirs.
36 hours ÷ 5 = 7.2 hours for one reservoir.
7.2 hours = 7 hours and 12 minutes for one reservoir.
