69
If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.
The smallest 5-digit integer perfect square is 10,000 = (100)2The largest 5-digit integer perfect square is 99,856 = (316)2So we want to know how many numbers that is, from 100 to 316 inclusive.It's 316 minus the first 99 = 217 of them.
There are 90 two-digit numbers from 10 to 99. Of those, 6 are perfect squares (16, 25, 36, 49, 64, and 81) and 2 are perfect cubes (27 and 64). Each perfect square or root has a probability of 1 in 90 in being drawn.
450.
961 961
If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.
102 = 100 which is the first possible three digit number that is a perfect square. 312 = 961 which is the last possible three digit number that is a perfect square. So there are 22 three digit positive numbers that are perfect squares.
12689 14689 12489
To find the two-digit numbers whose digits sum to a perfect square, we first identify the possible sums of the digits, which range from 1 (1+0) to 18 (9+9). The perfect squares in this range are 1, 4, 9, and 16. The valid two-digit combinations for these sums are: for 4 (14, 23, 32, 41, 50), for 9 (18, 27, 36, 45, 54, 63, 72, 81, 90), and for 16 (79). Counting all valid combinations gives us a total of 20 two-digit numbers.
none
4,624 = 682
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
With 123 digits you can make 123 one-digit numbers.
There are a lot of possibilities. The second digit can be 2 through 6, the third digit can be 3 through 7 as long as it is larger than the second digit. What we have so far: 1 _ _ 89
There are 5460 five digit numbers with a digit sum of 22.
Six: 0, 1, 4, 5, 6 and 9
5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.