Petals Around the Rose

Petals Around the Rose

Petals Around the Rose: ?

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Problem

Determine the rule used to calculate the number above from the dice<br>shown. Your only clues are the name of the game (Petals Around the<br>Rose) and the fact that the rule must be fairly simple, able to be<br>calculated at a glance by anyone who knows it.

You may reroll the dice as many times as necessary by clicking the<br>Reroll button, until you are confident know the rule. Then, click<br>Reveal Solution to see the full explanation.

Be warned though: you may only have one opportunity in your lifetime to<br>solve this problem yourself, so be certain you are<br>ready before revealing the solution!

Solution

Petals Around the Rose<br>is a very famous exercise in induction and lateral thinking. It is possible<br>to brute force it with enough rerolls, but the best approach is to look carefully<br>at what you are being shown and to think carefully about the context clues you are provided.

Definitions:

A rose is the center pip on a die face.

A petal is any pip on the outer edge.

The Rule:

The number shown is the total number of petals (edge pips) on dice with a<br>rose (center pip).

Explanation:

Only odd numbered faces can contribute to the total, but not all of them do. Going case by case:

1 has a rose, but no petals, so contributes nothing.

3 has a rose and a petal on each side, so contributes 2.

5 has a rose and a petal each corner, so contributes 4.

The even numbered faces (2, 4, and 6) do not have a center pip, so contribute nothing to the total.

Now that you have revealed the answer, petals will be shown in red; you may reroll to see other examples.

If you've read this far, you may also be interested in algorithmic approaches to solving the game with various machine learning techniques.

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