What 5 digit number (base 10) when multiplied by 9 yields the same number written "backwards."?

Question

Then PROVE IT IS THE ONLY ONE.

I dont know what you're thinking, but is the product of 11111 x 9 equal to 11111 (11111 written backwards)?

Answer 1

If a five digit number times 9 is another five digit number, then that five digit number must be less than or equal to 11111. For it to be a five digit number, it must also be >=10000. So the first digit must be 1. Hence, the last digit must be 9.

So our number is:

N = 1XYZ9.

We also know, since N<=11111, that X=0 or 1.

Note that 9*N + N = 10*N, so you can write this as the addition problem:

1XYZ9 + 9ZYX1 = 1XYZ90.

Looking at the tens digit, we see we get a carry over of 1 from the 1s digits, so we know that X+Z+1 has last digit 9. But since X=0 or 1, that means X+Z+1 = 9, or X+Z=8. In the 100s digit, Y+Y has last digit Z. In the 1000s digit, X+Z we know is 8, but we might get a carry-over from Y+Y of 1. So either Y=X+Z=8 or Y=X+Z+1=9. Since Y is always greater than 5, Y+Y always does contribute a 1 to the 1000s digit, so Y=9. Y+Y has last digit 8, which means Z=8 and X=0. So our number can only be 10989.

Answer 2

10989...

The number must be between 10000 and 11111, the original number must be a 5 digit number, and when multiplied by 9, it must still be a 9 digit number.

Since the first digit is a 1, you know that after you multiply by 9, the last digit must be a 1, which implies that the last digit of the original number must be a 9 (9*9 = 81). Use a similar method to find the rest of the digits.

Answer 3

10989 * 9 = 98901

The digits of any multiple of 9 must add up to 9!
Anything greater than 11111 results in a six-digit number when multiplied by 9.
Less than around 90000 results in a four-digit number when divided by 9.
Among the remaining possibilities, only one results in a reversal of digits!

Answer 4

to place in writing the proper, basically %. the numbers in descending orde. As in: 8= the optimal 5= 2d optimal 2= 0.33 higest a million= least you will get: 8521 because of the fact the proper obtainable kind. To get the backside, take care of the numbers in ascending order. As in: a million= the backside 2= 2d lowest 5= 0.33 lowest 8= optimal you will get 1258 because of the fact the backside obtainable quantity.t 2= 2d lowest 5= 0.33 lowest 8= optimal you will get 1258 because of the fact the backside obtainable quantity.

Answer 5

The answer is 10989 x 9 = 98901

Answer 6

11111

Answer 7

10989 * 9 = 98901

Answer 8

00000 * 9

Answer 9

hmmm.. dunno.. but.. try 11111 * 11111

or.. for that matter.. try 1111111 * 1111111