problem solving question?

Question

Find the digits A,B,C, and D that solve the following cryptharithm.

ABCD
x 4
-----------
DCBA

Answer 1

The answer actually is ABCD = 2178. The explanation is rather long though.

In case you care...

First of all, we'll refer to ABCD as the orig. num., and DCBA as the resultant. Since the resultant is only 4 digits long, the largest number ABCD can be is 9999/4 or 2499. This means that A can only be 0, 1 or 2. Since 4D then has to be some multiple of 10 plus 0, 1 or 2 ( i.e. 10, 2, 12, 31, etc...), we can immediately eliminate 1, because no odd number is evenly divisible by 4.

The only values of D which would allow A to be 0 are 0 and 5 (0 and 20 after multiplication). Similarly, if A is 2, D would have to be 3 or 8 (12 and 32). But if A=0 and D=5 then things won't work out, because if A is 0 the biggest original number is 999, and the biggest resultant would then be 3996, which means that D is not 5.

Moving on to the next possibility, if A=2 and D=3. There is no number between 2000 and 2999 that when multiplied by 4 will produce a number between 3000 and 3999 (try it if you don't believe me). This leaves us with only one choice... A=2 and D=8.

You can apply a similar strategy to the middle digits.

Tschuss!

Answer 2

1111

Answer 3

project fixing is two words, no longer a hyphenated be conscious. Too many human beings attempt to hyphenate $#it that doesn't choose hyphens. definite, that is human kin. nevertheless, it is likewise English communications and computing gadget operations.

Answer 4

they're all 0. that was easy

Answer 5

charely is wrong i think...if it was all the same number, it'd be AAAA not ABCD

Answer 6

0000

...which is basically 0