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Find the Number

Puzzle:

There is a five digit number ABCDE (A, B, C, D & E are 5 different single digit numbers). If you multiply this number with 4, you get reverse of the number. Find A, B, C, D & E respectively.

ABCDE * 4 = EDCBA


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Solution:

21978 * 4 = 87912

Look at the A in ABCDE. A can be only 1 or 2 because E can be 9 at the most. On the other hand, we look at the A in EDCBA. We found that A must be an even number, which should be 2. Since E x 4 produces a number within the one's place as 2, we know E must be 8. Since there is no carry from B x 4 to E's place, we know B must be 1. Since B = 1, we know D x 4 will produce a number within one's place as 8 so that 8 + 3 (carry) = 11. The only choice for D is 7. C can only be 8 or 9 to make the product of BC x 4 be close to DC. Since E is 8 already, C must be 9.
So ABCDE=21978


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7 comments:

abhishek said...

21978*4=87912

madhur said...

yepp you are correct no is
ABCDE =21978

think logically and you will reach the destination easily :P

A should be 2 and B should be 8

There shoudn't be any carry at A so B should either be 0 or 1(as 2 has already been used) but we can't get 0 at D after getting 3 as carry from E. So B has to be 1.

Now D has to be 7 coz (7*4 + 3) =31.(it could be 2 but it has already been used)

Now C has left with no option but 9.

A=2, B=1, C=9, D=7 and E=8

prashant said...

ya, its 21978.

Naresh said...

ya its 21978*4=87912

Akhilesh said...

21978

KT said...

yes the ans is

21978

KT said...

yipeeeeeeee.
iv done it.The ans is 21978