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Problems on the uniform distribution

(1) suppose U is a continuous uniform [0,1] random variable. what is the
probability that the decimal expansion of U contains no fives?

(2) What is the ...

Find the missing numbers

Given an array of size n. It contains numbers in the range 1 to n. Each
number is present at least once except for 2 numbers. Find the missing

Neighbourly Polyhedra

Can you construct 1000 internally disjoint convex polyhedra in R^3 any two of which share a face?

Tags: math geometry





Loaded Dice to Make Equally Likely Sums

We have two loaded dice, with 1,2,...,6 coming up with various (possibly different) probabilities on each. Is it possible that when we roll them both, each of the sums 2, ...