Number Problem

Find a number such that if we replace the first digit of the number with the last digit...the number doubles itself.

i think the answer is 00. I can't able to find the other answer..smartcoder give some clue... tell me howmany digit number that was..

---------------
suresh

Its not 0. I cnt tell u the number of digits!!

Correction in my problem :

Find a number such that if we [B]shift[/B]the first digit of the number with the last digit...the number doubles itself.

like if the number is abcdef
the doubled number should be fabcde

hi smart coder,

It is a time for giving your solution here....Otherwise give some other clue to solve this puzzle...

-------------------
suresh

there are 9 solutions each of 18 digits

Here is the answer for your question.....

Number : 052631578947368421

But this very difficult to find the answer....Here is some of the numbers i am work it out....

First of all i found the first digit should not greater than 4. Because if we use 5, after adding the number it is going to be extra one digit.

First i am trying the following numbers....

47389
double: 94778
one shift: 94738
difference: 40


42068
double: 84136
one shift: 84206
difference: 80

36747
double: 73494
one shift: 73674
difference: 180

31526
double: 63052
one shift: 63152
difference: 100

26345
double: 52690
one shift: 52734
difference: 44

21044
double: 42088
one shift: 42104
difference: 16

15763
double: 31526
one shift: 31576
difference: 50

10542
double: 21084
one shift: 21054
difference: 30

[B]051
double: 102
one shift: 105
difference: 3[/B] [B]Here i found i am going to the right way. In that time smart coder give the clue that is 18 digit number.[/B]

0521
double: 1042
one shift: 1052
difference: 10

052621
double: 105242
one shift: 105262
difference: 20

0526321
double: 1052642
one shift: 1052632
difference: 10

...
..

Using the same way finally i got the answer...But i don't know, is there any way to find the solution easily ?

--------------------
suresh

yes there is an easy way out, so i am putting up the solution

select any digit from 1 to 9. Suppose u selected 1.

Now I will double it. I get 2.
So my unit's digit is 2. again double it, I get 4
Now my number becomes 42.
Again I double 4.I get 8.
Now my number becomes 842.
So the logic is pick the leftmost digit ...double it and make it as the new leftmost digit(keep the carries aside)

now i take 8. Double it. I get 16. Now my number is
6842. carry = 1.
I take 6. double it. I get 12. Adding carry ( + 1) . I get 13. Now my number is
36842. carry = 1.

If we go on like dis we will reach at a stage like dis

5263157894736842 (carry = 0 )
take 5. double it. we get 10. Now my number is

105263157894736842 (carry = 0)
We end up wen we get the leftmost digit as the starting digit which we selected ( in this case it was 1) and carry = 0.

So here we get our number. U can check the condition over dis number.
Similarly select another digit initially and do the whole procedure with that digit. So there are 9 different answers.
Hope it was intresting!!