### Brain Teasers

# 0-1-1-2-10-_____-100903245677250689568

What 5-digit number completes the series:

0-1-1-2-10-_____-100903245677250689568

0-1-1-2-10-_____-100903245677250689568

### Hint

There is not a universally agreed definition of 0^0 (zero raised to the 0 power). This series relies on the most common definition:0^0 = 1

Without this definition the series can't start with zero. Starting the series with 1 yields:

1-1-2-6-226-2608759082

for the first six terms. The 7th term in this case has 48 digits starting with a 1 and ending with an 8.

### Answer

10018The first term 0 is arbitrary. If the terms are numbered starting at 1, then the nth term is the sum of each of the previous n-1 terms raised to the n-2 power.

0 = 0

1 = 0^0

1 = 0^1 + 1^1

2 = 0^2 + 1^2 + 1^2

10 = 0^3 + 1^3 + 1^3 + 2^3

10018 = 0^4 + 1^4 + 1^4 + 2^4 + 10^4

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