Brain Teasers
Rope
A man ordered a length of rope by telephone from his nearest hardware shop. But when he went to collect the rope, he found that the assistant had miswritten the order by interchanging feet and inches. As a result of this, the rope was only 30 percent of the length that the man wanted. So, what length did he want and what length did he get?
Answer
Ordered: 9 feet and 2 inchesReceived: 2 feet and 9 inches
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A very nice teaser. Well done!
You can set this up as an algebra problem, but using logic you can find the answer quickly.
To be an even 30% the total number of inches must be a multiple on ten; the inches and feet must both be less than 11; and the feet greater than inches times 10/3 and the inches not zero.
The feet/inches that are multiples of ten are:
1'8", 2'6", 3'4", 4'2", 5'0", 5'10", 6'8", 7'6", 8'4", 9'2", 10'0", 10'10", 11'8".
Applying the other requirements leaves only 9'2".
To be an even 30% the total number of inches must be a multiple on ten; the inches and feet must both be less than 11; and the feet greater than inches times 10/3 and the inches not zero.
The feet/inches that are multiples of ten are:
1'8", 2'6", 3'4", 4'2", 5'0", 5'10", 6'8", 7'6", 8'4", 9'2", 10'0", 10'10", 11'8".
Applying the other requirements leaves only 9'2".
3(12f + i)/10 = 12i + f => 26f=117i
i < 12
f and i are an integers
i < 12
f and i are an integers
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