How many distinct solutions are there to the alphametic
EO*OE=OEOE?

What if Itold you that the two partial products are:
OOO & EEE?

O & E stand for odd and even digits respectively.

There are 65 solutions for the alphametic EO*OE = OEOE:

21*50 = 1050, 21*58 = 1218, 21*70 = 1470, 67*16 = 1072, 21*52 = 1092, 61*18 = 1098, 87*14 = 1218, 41*30 = 1230, 25*50 = 1250, 43*30 = 1290, 81*16 = 1296, 47*30 = 1410, 25*58 = 1450, 29*50 = 1450, 27*54 = 1458, 81*18 = 1458, 49*30 = 1470, 41*36 = 1476, 83*18 = 1494, 23*70 = 1610, 43*38 = 1634, 21*78 = 1638, 23*72 = 1656, 47*36 = 1692, 61*30 = 1830, 25*74 = 1850, 21*90 = 1890, 27*70 = 1890, 63*30 = 1890, 43*70 = 3010, 41*74 = 3034, 61*50 = 3050, 43*72 = 3096, 65*50 = 3250, 63*52 = 3276, 47*70 = 3290, 61*54 = 3294, 61*56 = 3416, 49*70 = 3430, 69*50 = 3450, 47*74 = 3478, 67*54 = 3618, 63*58 = 3654, 41*90 = 3690, 41*94 = 3754, 43*90 = 3870, 65*78 = 5070, 67*76 = 5092, 61*90 = 5490, 61*92 = 5612, 63*90 = 5670, 81*70 = 5670, 81*38 = 3078, 83*70 = 5810, 81*72 = 5832, 65*90 = 5850, 61*96 = 5856, 81*90 = 7290, 81*92 = 7452, 83*90 = 7470, 81*94 = 7614, 83*92 = 7636, 85*38 = 3230, 85*90 = 7650, 87*90 = 7830

Yet, where the two partial products are: 000 & EEE, there is only one solution: 67*54 = 3618, with partial products 335 and 268.

(Thank you Charlie, I didn't use a program to find them, so am not surprised I missed those four).

Edited on October 17, 2014, 5:45 am

Posted by Dej Mar on 2014-10-16 15:00:38