# Dice Puzzle

The name of the game is Petals Around the Rose, and that name is significant. Newcomers to the game can be told that much. They can also be told that every answer is zero or an even number. They can also be told the answer for every throw of the dice that are used in the game. And that’s all the information they get.

The person who has the dice and knows the game, rolls five dice and remarks almost instantly on the answer. For example: in Roll #1 the answer is two.

Roll #1. 4 1 6 3 6

“The answer is what?” says the new player.

“Two.”

“On that roll?”

“Yes.”

“Would it still be two if I moved the dice without turning any of them over, just rearranging the pattern?”

“I can tell you only three things: the name of the game, the fact that the answer is always even, and the answer for any particular throw. In this case the answer is two.”

“So that’s how it is. What am I supposed to do?”

“You’re supposed to tell me the answer before I tell you. I’ll give you all the time you want, but don’t tell me your theory, just the answer. If you figure it out, you don’t want to give the idea away to these other jokers around you. Make them work for the answers, too. If you get the answer right on six successive rolls, I’ll take that as prima facie evidence that you understand the game.”

“OK, roll again.”

Roll #2. 5 6 5 4 4

“I give up. What’s the answer?”

“The answer is eight.”

“Roll again.”

Roll #3. 3 5 5 5 6

The answer is fourteen.

Roll #4. 2 6 2 1 4

The answer is zero.

Roll #5. 4 3 2 1 3

The answer is four.

Roll #6. 6 5 6 2 2

The Answer is ……?

The answer is four.

Remember, the name of the game is Petals Around the Rose, and the answer is always zero or an even number. To determine the answer, you need to look at the number of “petals” around the “rose” in each dice roll. A “rose” is a dot in the center of a die, and the number of “petals” is the number of dots surrounding the “rose” on each die. For example, in Roll #1, the number of “petals” is 4 (2 on each 6) and the answer is 2, which is an even number.

To determine the answer, count the number of “petals” on the dice that have a “rose” and then apply the following formula:

- If there are no “petals” (i.e., all dice show a 1), the answer is 0.
- If there are two “petals” (i.e., one die shows a 2, 3, or 4), the answer is 2.
- If there are four “petals” (i.e., one die shows a 5), the answer is 4.
- If there are six “petals” (i.e., one die shows a 6), the answer is 6.
- If there are eight “petals” (i.e., two dice show a 2, 3, or 4), the answer is 8.
- If there are ten “petals” (i.e., one die shows a 5 and one die shows a 2, 3, or 4), the answer is 10.

In Roll #6, there are four “petals” (two on each 6), so the answer is 4.

### Your Answer

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