SOLUTION: Aliaba was arranging the carpets for the flying carpet brigade. They were going to fly in a rectangular formation. When he put 4 carpets in each row, he had 3 left over. When he
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Question 460663: Aliaba was arranging the carpets for the flying carpet brigade. They were going to fly in a rectangular formation. When he put 4 carpets in each row, he had 3 left over. When he put 5 carpets in each row, he had 1 left over. How many carpets could there have been in the carpet brigade?
Use more than one way to present your solution(s). Answer by solver91311(24713) (Show Source):
To find the minimum number that has the characteristic that and set:
And solve. It should then be casual to the most obvious observer that since 4 times 5 is 20, that if you add any multiple of 20 to 11 you will get the same result.
Now we need to find a value such that is non-prime. That way, we can find a pair of integer factors and arrange the carpets in a rectangle with none left over.
11 is prime
31 is prime
51 NOT prime. 3 times 17 is a possible solution
71 is prime
91 NOT prime. 7 times 13...
There are infinitely more.
John
My calculator said it, I believe it, that settles it
