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.