When the great mathematician Ramanujam was in the UK, he once left his suitcase in a cab. His friend Hardy offered to help him trace the cab and called up the transport service. Incidentally, Ramanujam could not recollect the exact number of the cab but remembered a peculiar fact about the cab number. The number was a perfect square, and when read upside down, still made a perfect square.
Hardy called the cab company, and they told them that they had a flight of 400 cabs, numbered 001 to 450. Ramanujam, being a prodigy, immediately used this information to figure out the cab he had traveled in.
Can you guess what was the number on the cab that Ramanujam had left his suitcase in?
Answers
Given : The number was a perfect square, and when read upside down, still made a perfect square.
they had a flight of 400 cabs, numbered 001 to 450.
Ramanujam, being a prodigy, immediately used this information to figure out the cab he had traveled in.
To Find : Number of the cab
Solution:
cab numbered from 001 to 450
perfect square
001 , 004 , 009 , 016 , 025 , 036 , 049 , 064 , 081 , 100 , 121 , 144 ,
169 , 196 , 225 , 256 , 289 , 324 , 361 , 400 , 441 ,
Numbers can be read upside down with digit 0 1 , 6 , 8 and 9 only.
001 - 100 Perfect square
009 - 600 not perfect square
016 - 610 not perfect square
081 - 180 not perfect square
100 - 001 perfect square
196 - 961 Perfect square
361 - 193 not perfect square
We got three options:
001 - 100 Perfect square
100 - 001 perfect square
196 - 961 Perfect square
in first 2 options he can not identify that number was 001 or 100
But in last option number was 196 as 961 can not be the number of the cab as max number is 450.
Hence 196 was the cab number
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