These sets of numbers all follow logical patterns. Which numbers replace the question marks?

( 1, 8, ?, 64, 125 )

( 00001, 00011, 00101, ?, 01001 )

( 17,23,?,18,20,25,21,9,15,16 )

the second one is odd numbers.

the first one is I think powers of two, and the 125 should be 128.

..or the first one could be the cubes of natural numbers

1^3, 2^3, 3^3, 4^3, 5^3

00001, 00011, 00101, ?, 01001

1,3,5,?,9

? = 00111 This is Binary code converted to decimals

To find the missing numbers in each set, we need to identify the pattern or logic that governs the sequence. Let's work through each set one by one:

1) (1, 8, ?, 64, 125)

In this set, we can observe that each number is a cube.
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125

Therefore, the missing number is 27.

2) (00001, 00011, 00101, ?, 01001)

In this set, if we look closely, we can see that the digit in the middle alternates between 0 and 1.
00001 -> 0 0 0 0 1
00011 -> 0 0 0 1 1
00101 -> 0 0 1 0 1
01001 -> 0 1 0 0 1

Therefore, the missing number can be deduced as 01001, which represents the digits 0 1 0 0 1.

3) (17, 23, ?, 18, 20, 25, 21, 9, 15, 16)

In this set, the pattern is not as straightforward as the previous two. However, if we observe carefully, we can see that the numbers are grouped in pairs. The first number of each pair is a multiple of 3, while the second number is the result of adding 5 to the first number.
(17, 23)
(9, 15)
(18, 23)
(20, 25)
(21, ?)

From this pattern, we can deduce that the missing number is 23.

To summarize:
( 1, 8, 27, 64, 125 )
( 00001, 00011, 00101, 01001 )
( 17, 23, 23, 18, 20, 25, 21, 9, 15, 16 )