Puzzle 1
I recently asked my friend Alex to buy me some ribbon for my child's bonnet.
Alex went to the haberdashery shop for the required length, but accidentally swapped the feet and inches.
When I measured the resulting ribbon, I only had 5÷8 of the length I required.
How much ribbon did I originally ask for?
Remember that there are 12 inches in a foot.
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.
Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
(5 ÷ 8) x (12 x A + B) = (12 x B + A)
Simplifying gives:
A = (91 ÷ 52) x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.
B = 4 is the only possible value, which means that A = 7.
So I originally asked for 7 feet, 4 inches.
Double-Checking
I received 4 feet, 7 inches = 55 inches.
I asked for 7 feet, 4 inches = 88 inches, and 88 x (5 ÷ 8) = 55.
Puzzle 2
What are the next two numbers in this sequence:
202 122 232 425 262 728 {?} {?}
Puzzle Copyright © Kevin Stone
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Answer
293 031: these are the numbers 20, 21, 22, 23 etc grouped into three digits.
Puzzle 3
If I can boil 2 eggs in 10 minutes.
How long will it take me to boil 5 eggs?
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Hint
Be careful with your thinking.
Answer
Exactly the same time!
Puzzle 4
Which are there more of...
...square feet in half a square mile or cubic yards in a cubic furlong?
Puzzle Copyright © Kevin Stone
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Hint
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.
Answer
Square feet in half a square mile.
Reasoning
There are 3 feet in a yard, 1760 yards in a mile, and 8 furlongs in a mile.
A mile is 1760 x 3 = 5280 feet in a mile.
A square mile is 5280 x 5280 = 27878400 square feet.
Therefore half a square mile = 13,939,200 square feet.
A furlong is 1760 ÷ 8 = 220 yards.
Therefore a cubic furlong is 220 x 220 x 220 = 10,648,000 cubic yards.
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