一條數學題：ABCD＊４＝DCBA. ABCD=???

Since ABCD x 4 = DCBA, so ABCD must be smaller than 2500, or else the result will be a 5 digit number

A must be 1 or 2. since D x 4 = xA, A must be a even number, A=2
A=2, than D=3 or 8, but A=2, A x 4 = D, so D=8
C x 4 + 3 = yB
and B x 4 + y= zC, since A x 4 = D , we need to make z=0
B must be 1 since 3 x 4 =12, and 2 is used.
B = 1, than C x 4 + 3 = y1, 4C=10y-2, 2C=5y-1
4 + y = C, 8+2y=2C, 8+2y=5y-1, y=3, C=7
We have ABCD=2178
2178 x 4 = 8712

有步驟，詳細說明
但係睇英文，有d難頂=.=
不過冇問題，very good!!!

2178x4=8712

我以前做過這一條數學題,我查過,答案是2178
The ans:2178

Since ABCD x 4 = DCBA, so ABCD must be smaller than 2500, or else the result will be a 5 digit number



A must be 1 or 2. since D x 4 = xA, A must be a even number, A=2

A=2, than D=3 or 8, but A=2, A x 4 = D, so D=8

C x 4 + 3 = yB

and B x 4 + y= zC, since A x 4 = D , we need to make z=0

B must be 1 since 3 x 4 =12, and 2 is used.

B = 1, than C x 4 + 3 = y1, 4C=10y-2, 2C=5y-1

4 + y = C, 8+2y=2C, 8+2y=5y-1, y=3, C=7

We have ABCD=2178

2178 x 4 = 8712

ABCD = 2178

2178
x 4
______
8712

(這題數學題左在奧數華夏盃(四年級)出過!)

ABCD = 2178