Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Twin Chute-swapping Sudoku

By Henry Kwok

Twin B

Rules of Twin Chute-Swapping Sudokus

This Sudoku consists of a pair of linked standard Sudoku puzzles each with some starting digits.
As usual, the object of this Sudoku is to fill in the whole of each 9x9 grid with digits 1 through 9 so that each row, each column and each block contain all the digits 1 through 9.

Twin B is related to twin A in the following ways:
Given that twin A is the original puzzle, twin B is obtained by swapping a horizontal/vertical chute or band of blocks with another horizontal/vertical chute or band of blocks. By such transformation, twin A and twin B are essentially the same or equivalent Sudoku puzzle.

For example, fig 2 is created from fig 1 by shifting the first chute of 3 blocks sideways to the right and the second chute of 3 blocks sideways to the left.

Similarly an equivalent puzzle (fig 3) can be created from fig 1 by shifting the first chute of 3 blocks downwards and the second chute of 3 blocks upwards.

The three puzzles are equivalent to one another. Equivalent puzzles can also be created from fig 2 and fig 3 by similar transformations.