Showing what's behind the curtain

Investigate the game of chance involving colored discs.

Discover the largest product of thirteen consecutive digits in the 1000-digit number.

Find the first ten digits of the sum of one-hundred 50-digit numbers.

Find the number of routes from the top left corner to the bottom right corner in a rectangular grid.

Sum of the digits in 2^1000.

Find the sum of the digits in 100!

Find the first term in the Fibonacci sequence to contain 1000 digits.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle.

Find the distinct terms in the sequence generated by a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

Compose Champernowne’s constant