Puzzle 321
Are there more:
...square inches in a piece of carpet 15 yards by 5 yards
or
...feet in a 20-mile walk?
Puzzle Copyright © Kevin Stone
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Hint
There are 12 inches in a foot and 1,760 yards in a mile.
Answer
Feet in a 20-mile walk.
Reasoning
There are 12 inches in a foot, 3 feet in a yard, and 1,760 yards in a mile:
square inches in a piece of carpet 15 yards by 5 yards
(15 x 3 x 12) x (5 x 3 x 12) = 97,200 square inches.
feet in a 20-mile walk
20 x 1760 x 3 = 105,600 feet.
Puzzle 322
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 323
As I was going to St Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits.
Kits, cats, sacks and wives,
How many were going to St. Ives?
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Hint
Who was going to St Ives?
Answer
One.
Reasoning
Only I was going to St Ives.
This is a very old puzzle, and appeared in a manuscript dated around 1730. It is thought to refer to a town in Cornwall, UK.
If we were to count everyone and everything, including all of the kits, cats, sacks and wives, we would have:
Me = 1
Man = 1
Wifes = 7
Sacks = 7 x 7 = 49
Cats = 7 x 7 x 7 = 343
Kits = 7 x 7 x 7 x 7 = 2401
Total = 1 + 1 + 7 + 49 + 343 + 2401 = 2,802.
Puzzle 324
Our local scrap merchant had to travel to the county recycling plant, 60 miles away.
On the way there, the wagon was fully laden, so could only manage a steady 12mph.
On the way back, the wagon was much lighter and could manage a steady 16mph.
The wagon started with 24 gallons of fuel in the tank ready for the round trip, which was easily enough fuel as the wagon managed to travel 8 miles for each gallon.
Unfortunately, a piece of metal had pierced the fuel pipe at the very start of the trip, and the wagon began to lose 1 gallon of fuel every hour.
Luckily, it only lost fuel when moving and lost no fuel while unloading the scrap metal.
Were the 24 gallons enough for the entire round trip?
Puzzle Copyright © Kevin Stone
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Hint
How many hours was the truck travelling?
Answer
Yes.
Reasoning
The outward trip of 60 miles was at 12mph, so took 5 hours.
The return trip of 60 miles was at 16mph, so took 3.75 hours.
A total of 5 + 3.75 = 8.75 hours. In 8.75 hours, the wagon lost 8.75 gallons.
The total distance was 120 miles, which at 8 miles per gallon used 15 gallons.
So the total amount of fuel was 8.75 (lost) + 15 (used) = 23.75 gallons.
So the original 24 gallons was just enough.
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