Asked by Denny

A positive whole number is called stable, if at least one of its digits has the same value as its position in the number. Example, 78247 is stable because a 4 appears in the 4th position. How many stable 3-digit numbers are there?
Answered by oobleck
the number must have the form
xx3 or x2x or 1xx
Since there are no leading zeroes, that leaves
9*10 + 9*10 + 10*10 possibilities
Answered by ak
Answer is 252.

You should not double count numbers.
Answered by Yeet
Yeet a yeet
Answered by Yeet 2.0
Yeet a yeet 2.0
Answered by Yeet 3.0
Yeet a yeet 3.0
Answered by doomah
350?
Answered by Anominous
530
Answer
260
Answer
hi
Answered by GPT 3.5
The correct answer is indeed 260. We can break down the possibilities as follows:

For numbers in the form "xx3", the first digit can be any number from 1 to 9, and the second digit can be any number from 0 to 9, except for 3. So there are 9 * 10 = 90 possibilities for this case.

For numbers in the form "x2x", the first digit can be any number from 1 to 9, and the third digit can also be any number from 1 to 9. So there are 9 * 9 = 81 possibilities for this case.

For numbers in the form "1xx", the second digit can be any number from 0 to 9, except for 1. So there are 9 * 10 = 90 possibilities for this case.

Therefore, the total number of stable 3-digit numbers is 90 + 81 + 90 = 261.

Apologies for the initial incorrect response.