Puzzle 157
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 158
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.
Puzzle 159
Can you complete these common 5-letter words?
-S-G-
--R-F
-ZU--
E--X-
-P--C
--LN-
-W--M
---JO
Q---A
-V-K-
I--H-
-B-Y-
--DT-
Puzzle Copyright © Kevin Stone
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Hint
One of the words begins with the letter S.
Answers
-S-G- = USAGE
--R-F = SERIF
-ZU-- = AZURE
E--X- = EPOXY
-P--C = OPTIC
--LN- = KILNS
-W--M = SWARM
---JO = BANJO
Q---A = QUOTA
-V-K- = EVOKE
I--H- = ITCHY
-B-Y- = OBEYS
--DT- = WIDTH
Puzzle 160
Can you find common anagrams of the following words:
BINARY
ABROAD
RASCAL
ALTARS
BADGER
BARKED
MARBLE
UNABLE
TABLET
CALLER
Puzzle Copyright © Kevin Stone
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Hint
The first letters of the words are: B, A, S, A, B, B, R, N, B, C.
Answer
BINARY = BRAINY
ABROAD = ABOARD
RASCAL = SCALAR
ALTARS = ASTRAL
BADGER = BARGED
BARKED = BRAKED
MARBLE = RAMBLE
UNABLE = NEBULA
TABLET = BATTLE
CALLER = CELLAR or RECALL
There are some less common anagrams such as:
RASCAL = SACRAL
ALTARS = TARSAL
ALTARS = RATALS
ALTARS = TALARS
BADGER = GARBED
BARKED = DEBARK
MARBLE = BLAMER
MARBLE = AMBLER
MARBLE = LAMBER
UNABLE = UNBALE
TABLET = BATTEL
So you can have an extra half point if you found one of these! There are some even rarer anagrams, but I don't think I'll allow those!
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