_ _ _ _ _ × 8 = _ _ _ _ _
There is a number that you can put in the left-hand side of the above equation so that the blanks are filled in using every digit from 0 to 9 exactly once. What is that number?
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There is a number that you can put in the left-hand side of the above equation so that the blanks are filled in using every digit from 0 to 9 exactly once. What is that number?
There is more than one correct answer.
(10459, 83672), (10469, 83752), (10537, 84296), (10579, 84632), (10592, 84736), (10674, 85392), (10679, 85432), (10742, 85936), (10794, 86352), (10932, 87456), (10942, 87536), (10953, 87624), (10954, 87632), (12073, 96584), (12307, 98456), (12345, 98760)
Oddly enough, the numbers are 12345 & 98760. I knew that the first two digits of the top had to be low numbers, 1 and 2, so I just tried it out, and it worked!
This worked out well since the 1's digit of the multiplication (before carrying) ends up being 86420 (8 stepping down by 2), and we have carry values of 12340
So, we get:
8 - 0 + 1 = 9
8 - 2 + 2 = 8
8 - 4 + 3 = 7
8 - 6 + 4 = 6
8 - 8 + 0 = 0
A list of all the possible solutions to this:
(03187, 25496)
(04589, 36712)
(04591, 36728)
(04689, 37512)
(04691, 37528)
(04769, 38152)
(05237, 41896)
(05371, 42968)
(05789, 46312)
(05791, 46328)
(05839, 46712)
(05892, 47136)
(05916, 47328)
(05921, 47368)
(06479, 51832)
(06741, 53928)
(06789, 54312)
(06791, 54328)
(06839, 54712)
(07123, 56984)
(07312, 58496)
(07364, 58912)
(07416, 59328)
(07421, 59368)
(07894, 63152)
(07941, 63528)
(08174, 65392)
(08179, 65432)
(08394, 67152)
(08419, 67352)
(08439, 67512)
(08932, 71456)
(08942, 71536)
(08953, 71624)
(08954, 71632)
(09156, 73248)
(09158, 73264)
(09182, 73456)
(09316, 74528)
(09321, 74568)
(09352, 74816)
(09416, 75328)
(09421, 75368)
(09523, 76184)
(09531, 76248)
(09541, 76328)
(10459, 83672)
(10469, 83752)
(10537, 84296)
(10579, 84632)
(10592, 84736)
(10674, 85392)
(10679, 85432)
(10742, 85936)
(10794, 86352)
(10932, 87456)
(10942, 87536)
(10953, 87624)
(10954, 87632)
(12073, 96584)
(12307, 98456)
(12345, 98760)
Don't forget you can use 0 at the start of the first number :)