BMAD 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 comment Share on other sites More sharing options...

0 DeGe Posted September 26, 2013 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 comment Share on other sites More sharing options...

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## BMAD

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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