Four cubes Problem : Solution


And there rises the software engineer again in me.

This puzzle created by Franz Owen Armbruster in 1967, also called the “Instant Insanity” grabbed my interest when I was doing Artificial Intelligence for my Engineering majors last year.

Problem : Given to us are four cubes which are to be piled up on top of each other, such that all four colors appear on each side of the stack.

I studied the algorithm given by Robin Wilson, Professor of Geometry, Gresham College and wrote a computer program to implement the algorithm (which took me a few hours).

Four Cubes Problem – Gresham College Lecture

Solution : Let me briefly mention the algorithm for those of you who are a little lazy and don’t want to spend 5 minutes for the amazing illustration of this problem by Professor Robin Wilson.

We basically assign the colors Red(R – 1), Blue(B-2), Green(G-3) and Yellow (Y-5) with a number each, such that none of the numbers are divisible by each other. So each side of the combination of the four cubes will gives us a product of 30. ( = 30)


What I did was that I made a software which finds all the cases which satisfy the above condition.

We now enter the problem situation as input to the software :


Clicking on calculate will give us the result which we will interpret now.

The three rows (see the space along with the label Result) indicate the three possibilities which can form the solution. One row out of the three will be the front back of the cube while one out of the rest would be top and bottom.

Now let us examine the result :


If you can see the repetition GR, GR in Row 1 and Row 2, it would imply that Row 1 and Row 2 can never form a solution pair as we cannot have Green and Red as opposite ends in Front and Back as well as Top and Bottom, as that would violate the condition of having four different colors on four different visible faces of the cube.

Hence Row 1 would become front and back (marked in blue line) and Row 2 would form the left and right (marked in black line).

And here we are, we have solved this puzzle in less than 2 minutes.

I know this is a little complex but those who would set out to nail this problem would definitely find this useful.

Hope you guyz learnt something new today. Show off your knowledge about this puzzle to your friends.


Key :

LR = Left- Right
FB = Front Back
TB = Top Bottom

Download the Four cubes solution


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