Easy math puzzles
Poll
 | 23 votes (46.93%) | ||
| | 15 votes (30.61%) | ||
| | 7 votes (14.28%) | ||
| | 3 votes (6.12%) | ||
| | 12 votes (24.48%) | ||
| | 3 votes (6.12%) | ||
| | 6 votes (12.24%) | ||
| | 5 votes (10.2%) | ||
| | 12 votes (24.48%) | ||
| | 10 votes (20.4%) |
49 members have voted
6210001000.
Quote: WizardCan you find the one 10-digit "autobiographic number." Such a number describes itself with the number in each position, starting with 0, equaling the count of that digit in the whole number.
link to original post
Quote: charliepatrickThe logic I used was N210...010...0 works if you know how many zeroes there are, so there is one N. two 1s, and one 2.
6210001000.
link to original post
I agree!
Quote: WizardThis one is an old classic that may have been asked before.
Can you find the one 10-digit "autobiographic number." Such a number describes itself with the number in each position, starting with 0, equaling the count of that digit in the whole number.
For example, 1210 is one because:
There is 1 in in the 0 position and there is 1 numeral 0 in the entire number.
There is 2 in in the 1 position and there are 2 numeral 1's (that's an improper use of an apostrophe, Wiz) in the entire number.
There is 1 in in the 2 position and there is 1 numeral 2 in the entire number.
There is 0 in in the 3 position and there are 0 numeral 3's in the entire number.
Yes, the number is in base-10.
link to original post
I think this works:
6210001000
6x0, 2x1 1x2, 1x6
Is the answer really unique?
ETA: I guess I'm late with this answer. But I'm curious to see a uniqueness proof.
Quote: SkinnyTonyETA: I guess I'm late with this answer. But I'm curious to see a uniqueness proof.
link to original post
The source I got it from indicated it was the only 10-digit answer. I think I could prove no other first digit works.
D: 0 1 2 3 4 5 6 7 8 9
N: 6 2 1 0 0 0 1 0 0 0
P: 0 2 2 0 0 0 6 0 0 0
Note that the sum of Row N is 10 because it says how often each number appears, and so there are ten numbers in total.
Working along the N row , there will be six 0's, then two 1's, then one 2 etc. This also has to total to the ten digits. Hence the sum of the products, as in Row P, also has to be 10.
I suspect there's some kind of contradictory proof, for instance there cannot be 5 zeroes as that would mean there's a 1 under 5 and a total of 4 under numbers 1-4, so that the product is 5: 5xyz010000 etc. don't work.
