If you multiply a 4 digit #, ABCD by 4, the digits get reversed. that is
ABCD X 4=DCBA find ABCD (#'s cant repeat) I found out that 2469 is the largest and 1023 is the lowest.
I'm going to redo the entire thing for you and show you how to do it without using excel.
1. The range of the number is 1023<ABCD<2469
2. Make note that DCBA is divisible by 4
3. No number divisible by 4 ends in 1, therefore A cannot be 1, therefore A is 2.
4. D can be either 3 or 8 since both numbers multiply by 4 to a number that ends in 2, however in the number DCBA, we know that D has to be greater than or equal to 8 because 2 times 4 (4A) equals 8. Thus D is 8.
5. Because D has to be 8, it shows that 4B can't be greater than 10 because otherwise it would carryover and mess up the whole number. The only times that 4B is less than 10 is when B=1 or 2. As said in my previous post, combination BA must be divisible by 4 and end in 2. Therefore B must be 1.
6. Now use guess and check. But all you have to check is if C works when it's 3, 4, 5, 6, 7, or 9 (there is an algebraic way to find this but you have to ask yourself "is it really worth it")
Hello, blame_canada!
The reasoning is simpler than you think . . .
If you multiply a 4-digit number ABCD by 4, the digits get reversed.
That is: ABCD X 4 = DCBA. .Find ABCD.
Number the columns for reference.
I will use ? for a possible "carry".
Also, → will mean "ends with" . . . as in: 4 x 7 → 8Code:1 2 3 4 A B C D x 4 - - - - D C B A
In column-1, we have: 4 x A + ? = D
. . Hence, A = 1 or 2.
But if A = 1, column-4 says: 4 x D → 1 . . . which is impossible.
. . Therefore: A = 2
So we have:Code:1 2 3 4 2 B C D x 4 - - - - D C B 2
In column-1, we have: 4 x 2 + ? = D
. . Hence: D = 8 or 9.
In column-4, we have: 4 x D → 2
. . Therefore: D = 8 (and there is no "carry" from column-2)
So we have:Code:1 2 3 4 2 B C 8 x 4 - - - - 8 C B 2
If there is no "carry" from column-2, then B = 0 or 1.
If B = 0, then column-3 has: 4 x C + 3 → 0 ... which is impossible.
. . Therefore: B = 1
So we have:Code:1 2 3 4 2 1 C 8 x 4 - - - - 8 C 1 2
In column-3, we have: 4 x C + 3 → 1
. . Hence: C = 2 or 7
Since 2 is already used, C = 7Code:Solution 2 1 7 8 x 4 - - - - 8 7 1 2