Maths question

I think you would mean A, B, C, D are "digits " instead of "numbers " , right?

So in below, AB does not means A times B, it simply means digit A and digit B stick together (i.e. A x 10 + B)



Question 1: AB x CD = ABCD

I will show that there are no solution for this one

AB x CD
= AB x [100 - (100-CD)]
= (AB x 100) - [AB x (100-CD)]
= AB00 - [AB x (100-CD)]

Since A, B, C and D can't be 0 at the same time, AB>0 and CD>0

Therefore, AB x (100-CD) > 0

Now, AB x CD = AB00 - [AB x (100-CD)] < AB00

But AB00 < ABCD

Therefore, AB x CD < AB00 < ABCD

This is no solution for AB x CD = ABCD (except A=B=C=D=0, which is not allowed)



Question 2: AD x CB = ABCD

I find couple of answers... by computer ^_^ (since i have no idea how to find by hands...)

If A cannot be 0, then there are 2 solutions...

(i) 1395 ... [15 x 93 = 1395]
(ii) 2187 ... [27 x 81 = 2187]

If A can be 0, then there are 2 more...

(iii) 0126 ... [06 x 21 = 0126]
(iv) 0153 ... [03 x 51 = 0153]



Hope you still think that it is mathematics!!! (at least i think my answer to 1st question is mathematical) ^o^

(A)(B)X(C)(D) = AXBXCXD = ABCD
(A)(D)X(C)(B) = AXDXCXB = ABCD

so every munber can be satisfy the equation.