Puzzle #11: The 10-digit number

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.

Puzzle 11 Graphic

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!

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19 Responses to Puzzle #11: The 10-digit number

  1. Ramki says:


  2. JFfunCH says:


  3. Adhish says:

    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….

  4. Meetesh says:


    • Alok Goyal says:

      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!

  5. Meetesh says:

    Sorry, not a straight simple answer.. on second thoughts – 6210001000

  6. Ameya says:

    We got 6210001000!

  7. Vaishali says:


  8. Aman says:

    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?

  9. Manu says:

    Uhm…is it bad to leave solutions here?

  10. Arvind Mehra says:




  11. Arvind Mehra says:


    Regards, Arvind

  12. Arvind Mehra says:

    Alok, I think I had submitted yesterday but dont see it so doing it again.


    Regards, Arvind

  13. Neil says:


  14. pari says:

    Please expain how its comes 6210001000

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