4+4 Play Puzzle

This puzzle is an exchange puzzle by Karst Nauta for the International Puzzle Party 25 held in Helsinki, Finland 2005

Objective / Description:

Take all 3 pentacubes and select 3 of the 4 tetracubes to form a 3*3*3 cube. There are 4 possible combinations of 3 pentacubes and 3 tetracubes with which to make a 3*3*3 cube. Each of these 4 combinations has a unique solution.

About the puzzle:

The 4+4Play Puzzle results from a study of the Woody Woodpacker(*) universe. Indeed what makes this puzzle so special, is that although the total number of possible combinations of 3 pentacube plus 3 tetracube pieces with a single solution is no less than 6460, there are only 32 sets of the same 3 pentacube plus 4 tetracube pieces with single solutions for the

3*3*3 cube problem.

(*) Woody Woodpacker’s Innumerable Packing Problems (© Marcel Gillen and Georges Philippe, 1999) was my exchange puzzle at the IPP19 in London. The 3*3*3 cube problem was studied by Georges Philippe and Marcel Gillen, who not only computed the set of all combinations with a single solution (6460), but also found the subsets of sequential combinations both of 3 pentominoes and 4 tetrominoes (32) and of 3 tetrominoes and 4 pentominoes (112).

The +4 bonus:

Putting the pieces back in the box is another puzzle which can be solved in 4 different ways. Excluding rotations and symmetries, there are 4 different positions for the extra yellow cube to fill up the box.

Packaging: Wooden box

Preliminary estimate of shipping costs from the Netherlands.

Netherlands: from 0 - 2 kg, max. approx $ 12.00

Europe 1: from 0 - 2 kg, max. approx $ 23.00 to Belgium, Germany, France, (incl. Corsica and Monaco), Italy (excl. San Marino and Vatican City), Luxembourg, Spain (incl. Balearic Islands, excl. Canary Islands).

Europe 2: (rest of Europe) from 0 - 2 kg, max. approx. $ 32.00 to all other countries in Europe (excl. Russia).

ROW (rest of the world): from 0 - 2 kg, max. approx $ 43.00 – to all other countries (incl. Russia).

The final shipping cost will be determined when the item is closed.

And if more items are sold to the same address, the average shipping cost per item will be lower.