3

Part of 2006 Switzerland - Final Round

Problems(1)

sum of digits of 99x9999x...x99..99

Source: Switzerland - 2006 Swiss MO Final Round p3

Calculate the sum of digit of the number

9 \times 99 \times 9999 \times ... \times \underbrace{ 99...99}_{2^n}

where the number of nines doubles in each factor.

number theorysum of digitsDigits