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
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?
10 answers
Answer is 252.
You should not double count numbers.
You should not double count numbers.
Yeet a yeet
Yeet a yeet 2.0
Yeet a yeet 3.0
350?
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.
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
4 answers