### Brain Teasers

# Base Instinct

What is the missing value in the following list?

17 18 21 23 25 ? 101 122 10001

17 18 21 23 25 ? 101 122 10001

### Hint

This list ends at 10001. It does not continue to the right.Check the teaser's title.

### Answer

The missing value is 32.These are the representations of the decimal value 17 in decreasing number bases, down to binary.

Base 10: 1x10 + 7x1 = 17

Base 9: 1x9 + 8x1 = 17

Base 8: 2x8 + 1x1 = 17

Base 7: 2x7 + 3x1 = 17

Base 6: 2x6 + 5x1 = 17

Base 5: 3x5 + 2x1 = 17 <- Missing value 32

Base 4: 1x16 + 0x4 + 1x1 = 17

Base 3: 1x9 + 2x3 + 2x1 = 17

Base 2: 1x16 + 0x8 + 0x4 + 0x2 +1x1 = 17

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