A "Boggle"-ing Problem

Probability Level 3

In the game "Boggle", the standard game board consists of 16 cubes, each with 6 distinct letters on them. The player shakes the board to create a unique game board for each round. If shakes are totally uninfluenced and random, how many different possible game boards are there? (Disregard rotations of boards when calculating.)

Not intended to violate the copyright of Hasbro Inc©.

The answer is 2821109907456.

1 solution

Ritwik Tati
Jul 31, 2017

Relevant wiki: Permutations - Problem Solving

On a Boggle board, there are sixteen dice, each with six possible letters on each die. There are $36^8$ different permutations, or exactly $2821109907456$ possible boards

I didn't try to answer, just was curious to what you would answer and see as unique boards. Apparently rotations are not important in this question.

Peter van der Linden - 3 years, 10 months ago

It is clearly stated that rotations are disregarded when calculating.

Ritwik Tati - 3 years, 10 months ago

Hardly able to imagine I missed that. Sure you didn't at that later?

Peter van der Linden - 3 years, 10 months ago

@Peter van der Linden – At = add of course

Peter van der Linden - 3 years, 10 months ago

@Peter van der Linden – I don't think you can edit a problem after it's been posted, can you?

Ritwik Tati - 3 years, 10 months ago

@Ritwik Tati – Comments not, problems you can. But it was early in the morning for me. I regularly check problems then and not always solve them. I am interested in solutions and poins of views too. And I don't always have time or paper at hand to solve then and want to check of the idea I have might be in the solutions.

Peter van der Linden - 3 years, 10 months ago

@Peter van der Linden – A simple misunderstanding.

Ritwik Tati - 3 years, 10 months ago

A "Boggle"-ing Problem

The answer is 2821109907456.

1 solution

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