math puzzle?

Question

Assume each letter in the following formula represents a unique digit: (for example, ABCD could be the number 1234)

NOMAD x 4 = DAMON


What is the number represented by the digits DAMON?

Answer 1

NOMAD
x4
======
DAMON

Looking at the 5th digit column we find that since N is the units digit of something multiplied by 4,it must be even. But since DAMON and NOMAD have the same number of digits, we know that N * 4 < 10 ... or N<3. So N must be 2.

Looking If N=2, going back to the first digit we find that D must be 8 or 9 (depending on if the second digit column carries). But since we know that D *4 ends in 2, D must be 8 (9*4 ends in 6).

So we have:

2OMA8
x4
======
8AMO2

Now since D=8, we know that the 2nd digit column did not carry, so O * 4 < 10. Therefore O is 0,1,or 2. Butlooking at the fourth column we find that O must be odd, as it had three carried over from the fifth column (8*4 = 32) and that three is added to an even number (the last digit of A * 4 would be even). This means O must be the only odd number in {0,1,2} . So O = 1

Looking at the fourth digit column, this means that A*4 ends in 8 (as when the 3 is carried over the result is 1). The only two choices that when multiplied by 4 result in 8 are 2 or 7. But we've already used 2 for N. Therefore A = 7.

21M78
x4
======
87M12

We just need to figure out the 3rd digit column. The column has 3 carried into it (78 *4 = 312), It also carries out 3 (87 = 21 *4 + 3).

So:

M * 4 + 3 = 30 + M
3M = 27
M=9

21978
x4
======
87912

The number represented by DAMON is 87912.

Answer 2

N has to be even and no greater than 2. So it is 2.

D is 8 or 9. But looking at 4D, D from those two choices has to be 8.

O can only be 0 or 1; else D couldn't be as small as 8.

I'm bored already, and this is a well-known problem. I may come back and edit in a complete solution later.

Answer 3

this is named a good judgment puzzle or good judgment difficulty. Penny Press sells magazines of them on the link under; Kappa's link would not look to paintings besides. they're greater fee-effective in magazine form than e book form.

Answer 4

I don't know, but 40 years ago I and my father spent ages trying to work out a newspaper puzzle which said:

2 x WRONG = RIGHT

I still don't know the answer!

Answer 5

21978 x 4 = 87912

Answer 6

yea i have solve it!!! hmm one of let take D=0 then
NOMA(0)*4=0AMON
and the answer is 0=0

it is so simple!!!!!!!!!!!

Answer 7

60645656.....is that right???????