The Number Puzzle

Number Theory Level 3

Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.


The answer is 6210001000.

Payal Sheth by Payal Sheth , 22, India

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3 solutions

Ankit Kumar Jain
Feb 1, 2015

You just have to try the number of zeroes:

1) 9 zeroes are not possible - 9000000001.

2) 8 zeroes are not possible - 8100000001.

3) 7 zeroes are not possible - 7210000010

But ,

6210001000 is possible.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kenny Lau
Jul 8, 2014

Here is my mind while guessing:

9,000,000,000

9,000,000,001

9,100,000,001

9,120,000,001

6,120,000,001

6,120,001,000

0 Helpful 0 Interesting 0 Brilliant 0 Confused

nope.. there are 2 1's in your number.. but you have '2' in the place of how many 1's.. sorry if i confused you but i don't know how to say it oops

Payal Sheth - 6 years, 11 months ago
Payal Sheth
Jun 22, 2014

Its just a little bit of thinking. As far as I tried, I wasn't able to get a proper solution.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Could it be 7100000100?

Sourayan Banerjee - 6 years, 11 months ago

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No it can't be because the second digit should be 2.

Adarsh Kumar - 6 years, 11 months ago

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