6 6 1 2 + 2 -> Invert -> + 1 9 9 |        | On a calculator, the digits 0,1,2,5,6,8,9 can all be inverted and still
be readable as numbers. (6 and 9 become each other and all other digits
are unchanged. In the example at left, the entire column can be inverted
and the sum (the lowest row) is still valid. Can you find an example where at least one summand uses two or more different digits? All summands should have the same number of digits. Leading zeros are allowed, and you could use two or more summands (the example uses three.) |
From Joseph DeVincentis, same when inverted: 065 525+ 590 From Mark Rickert: No carry between columns in this discussion of an infinite number of solutions. The top row consists of any combination of 0s, 1s, 2s, 5s, 6s, and 8s.. The bottom row is the same as the top row, but the 6s are replaced with 9s. There can be any positive number of interior rows. The interior rows consist of the digits 0, 1, and/or 2 such that for each column: - if the top/bottom numbers are 0/0, 1/1, 2/2, 5/5, or 8/8, the interior numbers are all 0 - if the top/bottom numbers are 6/9, the interior numbers sum to 3 using the digits 0, 1, and/or 2. For example: 66860566612 21666506866 12020011000 00220001001 11000020100 00102000011 +10010002200 +00011002021 99890599912 21999509899 From Denis Borris: An example of four 3-digit numbers: a: 616:616 b: 121:182 c: 182:121 d: 919:919