Showing what's behind the curtain

How many 8 × 8 chess boards are embedded in a painting which consists solely of black and white squares, arranged in a checkered pattern

Answers and techniques for solving the Impossible Test Christmas. Revised for newest version 1/17/2013

Comparing four-sided and six-sided dice

Find the sum of the distinct square-free numbers in the first 51 rows of Pascal’s triangle.

Find the unique positive integer for a concealed square.

Skew-cost coding

Tribonacci non-divisors

An Arithmetic Geometric sequence

Odd triplets in Pascal’s triangle.

Find fractions that cannot be cancelled down (resilient fraction).