Brain Teasers
Four Consecutive Natural Numbers
The product of four consecutive natural numbers is 9???4, and we don't know what the ?s are. Find the largest number of the four.
Answer
The product of four consecutive natural numbers end with a 4, therefore none of them can end with 5 or 0, and their unit digits can be only 1, 2, 3, 4 or 6, 7, 8, 9.Since 20^4=160000 and 15^4=50625, they can only be 16 through 19, and we check that 16*17*18*19=93024.
Therefore, the largest number of the four is 19.
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Comments
Sep 26, 2007
I just did guess and check and it wasn't as hard as I thought it would be.
I tried solving it algebraically, but that didn't work, so I got it using trial and error. Good teaser!
I estimated the four numbers using the 4th root (sqrt twice) and guessed it right away! This is a very good math teaser, and really fun!
I estimated the four numbers using the 4th root (sqrt twice) and guessed it right away! This is a very good math teaser, and really fun!
*Groan!* My comment didn't plot first, then it showed up twice! Sorry!
I did it the same way it was explained except since I was doing it in my head I used 10^4 instead of 15^4 for the approximation.
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