21 replies to this topic

[rookie1ja]

10-digit Number - Back to the Number Puzzles

* Find a 10-digit number, where the first figure defines the count of zeros in this number, the second figure the count of numeral 1 in this number etc. At the end the tenth numeral character expresses the count of the numeral 9 in this number.
* Find a 10-digit number, where the first numeral character expresses the count of numeral 1 in this number, ..., the tenth numeral the count of zeros in this number.

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
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Spoiler for Solution

10-Digit Number - solution
* Sum of all numerals must be ten because each numeral stands for the count of other numerals and because this number shall have ten numerals. Beginning to choose reasonable numerals for the first figure you can come across the correct number: 6210001000.
* 2100010006.

[Incognitum]

I don't understand the question very well. What is a 'count of zeros,' there should only be one zero in this number right?

You can tell me if I've got it right...

We need a ten digit number: XXX-XXX-XXXX

And the value of the first digit gives the placement of the number 0, for example: 5XX-X0X-XXXX.

Is that what you're looking for?

[Incognitum]

Oh, I think I understand, you're looking for these numbers?

6210001000

2100010006

[Incognitum]

Yes, the part I don't understand is why it was two separate questions. The value of the zeros doesn't change when you change the digit where you count them. That's why I originally thought you were looking for the position of each, because you move the position in the second half of the question.

[rookie1ja]

feel free to reword the puzzle to make it more comprehensible

[jailbreak]

9000000000

[mdsl]

9000000000

so there's nine 0s and zero 9s?

[sanjay_kv]

6210001000.

Follow the process of substitution starting with 9000000000.
9000000000 --> 8000000010 --> .... --> 6210001000.

[leo78]

Which part of the question said all 10 digit must add up to equal to 10?

[mdsl]

Which part of the question said all 10 digit must add up to equal to 10?

Logic says that. If each place value (billions' place through ones' place) is a count of how many times a numeral (0 through 9) appears in the 10 digit number then the sum of the digits will equal 10 because because there are only 10 numerals to be counted.