Design an image that visually describes a mathematical concept related to the position and value in numbers. Show a three-digit number where each digit position hosts little spheres. Each sphere should have its positional number etched on it, but the etching should not be seen as text. The rightmost sphere should be glowing differently, signaling its uniqueness and stability due to its matching positional value. Ensure the background hints to a numerical landscape without intruding the central concept.

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?

Answer is 252.

You should not double count numbers.

Yeet a yeet 3.0

530

260 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.

hi

Yeet a yeet

Yeet a yeet 2.0

350?

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