Jump to content
BrainDen.com - Brain Teasers
  • 0

Even Odd multiplication



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:


x E E


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


What was the original problem?

Link to comment
Share on other sites

1 answer to this question

Recommended Posts

  • 0

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

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.


  • Recently Browsing   0 members

    • No registered users viewing this page.
  • Create New...