jasen Posted October 28, 2015 Report Share Posted October 28, 2015 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.Find the sum of all the multiples of 3 or 5 below 1000.It is easy to find the answer using computer, but it's more interesting if we can solve it without coding. Quote Link to comment Share on other sites More sharing options...

0 Rob_G Posted October 28, 2015 Report Share Posted October 28, 2015 So...The multiples of 3 are all of the form 3n where n is a natural number. The largest value of n is floor(1000/3) or 333. So we get 3(1), 3(2), 3(3), ..., 3(333). So if we sum them...sum[n=1...333](3n) we get 3* (333*334)/2 or 166,833.The same follows for 5 1000/5=200. So sum[n=1...200](5n) or 5*(200*201)/2 or 100,500.Finally we add them together to get 267,333. Quote Link to comment Share on other sites More sharing options...

0 jasen Posted October 28, 2015 Author Report Share Posted October 28, 2015 So...Hidden Contentgood start but wrong, your way to find out sum of multiple 3 and 5 are still wrong. Quote Link to comment Share on other sites More sharing options...

0 Thalia Posted October 28, 2015 Report Share Posted October 28, 2015 Adding on to Rob_GEvery 15 (3*5), you get a duplicate number. 66 multiples of 15 in 1000. So if we follow the same method used for 3 and 5, we get 15(66*67)/2=33,165. Subtracting this from 267,333, we get 234,168. Quote Link to comment Share on other sites More sharing options...

0 jasen Posted October 28, 2015 Author Report Share Posted October 28, 2015 Adding on to Rob_GHidden Contentvery close! just wrong 1 digit.the question is asking for sum bellow 1000. Quote Link to comment Share on other sites More sharing options...

1 Thalia Posted October 28, 2015 Report Share Posted October 28, 2015 Oops. 1 extra multiple of 5 then. So we subtract 1000 and get 233,168. Quote Link to comment Share on other sites More sharing options...

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## jasen

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

It is easy to find the answer using computer, but it's more interesting if we can solve it without coding.

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