What 4 numbers mulitplied by 4 gives you the same numbers backwards?

Answer 1

4 * (ABCD) = DCBA

Since D is a single digit and therefore less than 10, A < 2.5

A is even, since it is the final digit in the number divisible by 4

Therefore, A = 2

In order to make A = 2, 4*D must end in 2, therefore D = 3 or 8

However, since A = 2, D must be at least 8.

Therefore D = 8

Since A = 2 and D = 8, 4 x B < 10, therefore B is less than or equal to 2.

Also, since D = 8 and 4 x 8 = 32, the units of (4C+3) must equal the units of B.

Therefore, since (4C+3) is always odd (even plus odd), B is odd.

Therefore B = 1

So far, we have 4(21C8) = 8C12

Since 4 * 2 = 8, we also know that 4 * (1C8) = C12.

We can also infer, from knowing that 4 * 1 = 4 and 4 * 2 = 8, C is at least 4 and smaller than 8 (since 1C8 greater than 100 and less than 200)

But, since 8 * 4 = 32, 4(10 + C) = 10 * C + 1 - 3, therefore 4(10 + C) = 10*C-2).

We can therefore rearrange to get 6C = 42

Therefore C = 7

ABCD = 2178

Final check:

2178 * 4 = 8712