This is a very nice puzzle I picked up a few days back from one of the Martin Gardner books. I also tried it with my 8 year old, who solved it with some persuasion.
In the 10 cells of the figure above, inscribe a 10-digit number such that the digit in the first cell indicates the total number of zeros in the entire number, the digit in the cell marked “1” indicates the total number of 1’s in the number, and so on to the last cell, whose digit indicates the total number of 9’s in the number. Zero is a digit, of course. The answer is unique.
For children, ask them to solve the same puzzle with 4 digits and 5 digits first before going on to 10 digits.
Happy puzzling!
Alok Goyal's Puzzles Page 
9100000000
Wrong answer Ramki. There are only 8 zeros in your answer. Keep trying!
6210001000
Nice one Alok! Worked on it with my son… We came up with 6210001000.. Same pattern works on 9,8,7 digits but not 6..then again with 5 and 4….
9000000000
Hi Meetesh, good to see you on the puzzle blog. Unfortunately the wrong answer. There is a 9 in your answer but there is a 0 being shown in digit 9. Keep trying!
Sorry, not a straight simple answer.. on second thoughts – 6210001000
We got 6210001000!
6210001000
Would the number under a specifc number also count towards the total count – for e.g there could be a 1 under 7 – which would lead to a 1 under 1 – this would actually lead to a count of 2 ones?
Yes
6210001000
Uhm…is it bad to leave solutions here?
Alok,
8000000010
-Arvind
sorry..this is wrong.let me try again.
6210001000
Regards, Arvind
Alok, I think I had submitted yesterday but dont see it so doing it again.
6210001000
Regards, Arvind
6210001000
Please expain how its comes 6210001000
did you look at the answer?