## Sunday, January 14, 2007

### OEE*EE = OOEE

The above is a mathematical puzzle sent by one of friends. "O"s are odd numbers and "E"s are even numbers in the puzzle. The expression made me think of some english words.

(Opportunity,Expertise,Enablers)*(Excitement,Effort) = Ovation, Outstanding achievement, Efficiency, Effectiveness)

Some more "E"s which also can be used are Education, Experience, Eagerness, Enthusiasm, Energy

kvssnrao
on the day of Makara Sankranti
14th January 2007

explorer said...

this is just in case the problem is yet to be solved .. in case the solution is already at hand, there's no point in trying to figure out where to start from..

let the prob be 01e1e2*e3e4=o2o3e5e6
(numbering the o's and e's for easy referencing)
on a quick glance 01 can be 1 with e3 upto 8 (i.e 2,4 ,6,8) or o1 = 3 with e3 = 2 because the result is a four digit no.
further e5 can be a sum of two evens or two odds .. but since e3 *e2 will be even so e5 is sum of two evens .. this means e1e2*e4 will have units and tens digits as even .. this implies the carry over if any from e2*e4 is not odd .. the combinations for (e2,e4) thus are 2,2; 2,4; 4,2; 4,6; 6,4; 6,8; 8,6; 8,8.

it is assumed that zero is neither even nor odd.
usually such problems have added clarification that no number is repeated , one such in this case also shall greatly reduce the possible combinations thus simpifying the problem .. is this a case here? pl clarify. can the use of different words for o's and e's be taken as a hint for nonrepeating nos.?

KVSSNrao said...

Thanks for detailed explanation. Somebody from the group solved the puzzle immediately.