BMAD 65 Posted September 25, 2013 Report Share Posted September 25, 2013 We have two numbers that multiplied together to produce another number. All of the digits were replaced with E for the even numbers and O for the odd numbers, showing the following setup: O E E x E E E O E E E O E note the use of x as the operator of times. O O E E What was the original problem? Quote Link to post Share on other sites

0 Solution DeGe 9 Posted September 26, 2013 Solution Report Share Posted September 26, 2013 Nice puzzle 348 x 28 Here's why: Lets rewrite the puzzle as: o1 e1 e2 e4 e3 e8 o2 e6 e5 e9 o3 e7 o5 o4 e10 e5 o1 must be less than 5 because e4 multiplied by oee is 3 digit number o1 is either 1 or 3 If o1 is 1, then the multiplication of oee with e3 with end in 1xxx So, o1 must be 3 Then e4 must be 2 in order to keep oee x e4 a 3 digit number e9 is 6 then e8 must be 2 and o5 must be 9 if e8 is2, then e3 is either 6 or 8 If e3 is 6, the carry over needed from e1xe3 is either 3 or 5 in order to get e8o2 as 21 or 23 Then e1 must be 6 or 8 However, e1 must be either 2 or 4 otherwise e9 will not be even So e3 can not be 6 e3 must be 8 If e3 is 8, e1 can be 2 or 4 Also e2 must be either 6 or 8 because if e2 is 2 or 4, it gives an odd carry over and e6 will then not be even Now, if e1 is 2, carryover sent to multiplication of 3x8 will be 2 (16 + either 4 or 6 carried over from 6x8 or 8x8) and o2 will not be odd so e1 must be 4 Finally, for e2 which is either 6 or 8 If it is 6, the individual multiplications of oee with e4 and e3 are ok; However, if you add them up, it results in OEEE instead of OOEE With e2 as 8, all the results are ok Quote Link to post Share on other sites

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## BMAD 65

We have two numbers that multiplied together to produce another number. All of the digits were replaced with E for the even numbers and O for the odd numbers, showing the following setup:

O E E

x E EE O E E

E O Enote the use of x as the operator of times.O O E E

What was the original problem?

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