Puzzle 1
Using all of the letters A to Z, each once only, complete these common words.
-e-er
--eue
--o
ma-
-p-a-e-
-erso-
---k-am-on
-ouse
-a-
-ur-
---igent
Puzzle Copyright © Kevin Stone
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Hint
The first word begins with the letter F.
Answer
-e-er = fever (FV)
--eue = queue (QU)
--o = zoo (ZO)
ma- = mat (T)
-p-a-e- = speaker (SEKR)
-erso- = person (PN)
---k-am-on = backgammon (BACGM)
-ouse = house (H)
-a- = wax (WX)
-ur- = jury (JY)
---igent = diligent (DIL)
This puzzle isn't guaranteed to have a unique answer, can you find another?
Puzzle 2
What number comes next in this sequence:
1 4 8 13 21 30 36 ?
Puzzle Copyright © Kevin Stone
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Hint
Try writing the numbers out as letters.
Answer
45.
Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1 + length("ONE") = 4
4 + length("FOUR") = 8
8 + length("EIGHT") = 13
13 + length("THIRTEEN") = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY") = 36
36 + length("THIRTYSIX") = 45
Puzzle 3
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 4
Place an arrow in each empty square.
Every arrow can either point left or right, but must point to a square with a number.
The numbers indicate the total number of arrows that point at them.
Puzzle Copyright © Johan de Ruiter
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Hint
2 arrows point to the right, and the others point to the left.
Answer
