Petals Around the Rose

Petals Around the Rose: ?

Problem

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

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

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

Solution

Petals Around the Rose is a very famous exercise in induction and lateral thinking. It is possible to brute force it with enough rerolls, but the best approach is to look carefully 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 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.