I'm the number- 1
Number Theory
Level
2
Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
The answer is 3211000.
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1 solution
I kind of did this by trial and error:
If I start with a 1 , there can only be one 0: 1_ _ _ _ _ 0 and therefore I'd need at least a 5 somewhere, because the 6th digit can't be 0! (Obviously I want the 0 at the end because otherwise I'd need to have a 6 somewhere, which would mean I have 6 digits of the same kind which I clearly can't have, because I only have 5 places left (they cant be all 0's because the first digit is a 1.))
If I start with a 2 , there can only be two 0's: 2_ _ _ _ 0 0 and therefor I'd need at least 5 somewhere, because the 5th digit can't be 0. (Here I also want the 0's at the end, because of the same logic.)
Starting with 3 : 3_ _ _ 0 00, then I have one 3, therefore: 3_ _ 1 000. Here you can just see if I put a 1 in second place this 1 wouldn't be correct: 3 1 _ 1000 (now we have two 1's, but 2nd digit is a 1, therefore this doesn't work!!) so I need to put a 2 there: 3 2 _1000 Now we can see that we NEED to put a 1 in the missing spot: 3211000
Thank you for reading, constrictive criticism appreciated! :)