#22

COMPLETE the following row of numbers: 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, 121, 10000, ?

Answer:

1 111 111 111 111 111
Yes, a very large number indeed! That's 16 ones in a row. And why? Well, think about the word 'COMPLETE' in the riddle. It means the row contains 16 numbers. So the row probably has something to do with the number 16.And how do these numbers relate to 16? Well, each number is actually equal to 16, but written in another numerical system. For example: 16 in the hexadecimal system is written as 10 (1x16 + 0x1). Let's go over the list:
16 in the 16th (=hexadecimal) numerical system is 10 (1 times 16 + 0 times 1)
16 in the 15th numerical system is 11 (1 times 15 + 1 times 1)
...
16 in the 3rd numerical system is 121 (1 times 9 + 2 times 3 + 1 times 1)
16 in the 2nd (binary) numerical system is 10000 (1 times 16 + 0 times 8 + 0 times 4 + 0 times 2 + 0 times 1)
and finally 16 in the 1st numerical system is 1111111111111111 (1 times 1 + 1 times 1 + ... + 1 times 1)