Brain Teasers
Oranges 2
Lester has a number of oranges that he has to put into a box. He finds that when he puts them 2 at a time, 1 remains; when he puts them 3 at a time, 2 remain; when he puts them 4 at a time, 3 remain; when he puts them 5 at a time, 4 remain; when he puts them 6 at a time, 5 remain. However when he puts them 7 at a time, none remain. Can you find the number of oranges he has?
Answer
Lester has 119 oranges.There are probably a few ways to solve this, but one way is to first find multiples of 7 that are not multiples of 2, 3, 4, 5 or 6. This will narrow down your search, and then you can use trial and error to find the answer.
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Comments
119 is the smallest but not the only solution. In fact any number of the form 420n+119 where n is a non-negative integer will work. (so 539, 959, etc. are solutions). In essence, x is a solution if and only if x is divisible by 7 and x+1 is divisible by 60 -- because 60 is the least common multiple of 2,3,4,5, and 6.
Thanks NYJFan196 for giving your comments. I noted them down.
Great teaser. It was really hard and I understood the answer.
I should have been able to do this but.....it is late at night. Anyone want to post up a general comment explaining the "119" in terms of the factors and the remainders?
I rated this easy as there are many ways to retrieve the soultion.
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