## Poll

7 votes (53.84%) | |||

5 votes (38.46%) | |||

3 votes (23.07%) | |||

2 votes (15.38%) | |||

6 votes (46.15%) | |||

1 vote (7.69%) | |||

2 votes (15.38%) | |||

2 votes (15.38%) | |||

7 votes (53.84%) | |||

5 votes (38.46%) |

**13 members have voted**

When Pinocchio lies, his nose gets twice as long. When he tells the truth, his nose gets 1 cm shorter.

His nose was 1 cm long in the morning, and it is 100 cm long in the evening.

What is the least possible number of times he opened his mouth today?

Quote:GialmereWhen Pinocchio lies, his nose gets twice as long. When he tells the truth, his nose gets 1 cm shorter.

His nose was 1 cm long in the morning, and it is 100 cm long in the evening.

What is the least possible number of times he opened his mouth today?

10 times, in this order:

Lie (2 cm), lie (4), lie (8), truth (7), lie (14), truth (13), lie (26), truth (25), lie (50), lie (100)

Quote:ThatDonGuy

10 times, in this order:

Lie (2 cm), lie (4), lie (8), truth (7), lie (14), truth (13), lie (26), truth (25), lie (50), lie (100)

Correct

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Voldemort: So I need to lie?

Pinocchio: Yup!

After your earlier trials, you've come up with an idea for a casino dice game.

The player rolls one black die and one red die. If the black die gives an odd number, the player's overall score is zero. If the red die gives an even number, the player rolls it again and again until it is odd. The player's score is the sum of the two numbers, except for the previously mentioned case.

What is the average player score for this game?

Quote:Gialmere

After your earlier trials, you've come up with an idea for a casino dice game.

The player rolls one black die and one red die. If the black die gives an odd number, the player's overall score is zero. If the red die gives an even number, the player rolls it again and again until it is odd. The player's score is the sum of the two numbers, except for the previously mentioned case.

What is the average player score for this game?

I’m assuming that if the black die is even and the red die is even, then only the red die and not the black die is rolled again. If that’s right I get:

Quote:unJon

I’m assuming that if the black die is even and the red die is even, then only the red die and not the black die is rolled again. If that’s right I get:3.5

You assume correctly and your answer is...

Correct

[A player would probably need to score at least 5 points to be in the money.]

--------------------------

At a board game shop...

Customer: I want a dice.

Clerk: The correct term is 'die'.

Customer: I want 2 die.

Clerk: Plural is dice, alone it's die.

Customer: I want 2 die alone.

Quote:Gialmere

After your earlier trials, you've come up with an idea for a casino dice game.

The player rolls one black die and one red die. If the black die gives an odd number, the player's overall score is zero. If the red die gives an even number, the player rolls it again and again until it is odd. The player's score is the sum of the two numbers, except for the previously mentioned case.

What is the average player score for this game?

So help me out on this....I tried to set it up like a typical dice throwing outcome chart, and then form a geometric series.

Pair of dice throw once (black die - y axis and red die - x axis) with sum outcomes:

1 2 3 4 5 6

1 0 0 0 0 0 0

2 3 4 5 6 7 8

3 0 0 0 0 0 0

4 5 6 7 8 9 10

5 0 0 0 0 0 0

6 7 8 9 10 11 12

The average of these outcomes = 3.75, so then I did a geometric series where a=3.75 and r = .5 (for 50% chance of rolling an even number on red die). this would give me 3.75/(1-.5) which comes to 7.5.

Maybe I assumed that both dice would continually be rolled over again until an odd number on the red? I'm also on my 2nd beer already though (took a long 4th of July weekend).....!

Thanks for your help!

The probability of a 0 is 3/6 = 1/2.

If it is not 0, there are three options for black: 2, 4 and 6 and there are three options for red: 1, 3 and 5.

There are nine possible sums:

2 + 1 = 3

2 + 3 = 5

2 + 5 = 7

4 + 1 = 5

4 + 3 = 7

4 + 5 = 9

6 + 1 = 7

6 + 3 = 9

6 + 5 = 11

So the average score is...

0.5 x 0 + 0.5 x (3 + 5 + 7 + 5 +7 + 9 + 7 + 9 + 11) / 9 =

0.5 x 63 / 9 = 3.5

Quote:Gialmere...The player rolls one black die and one red die. If the black die gives an odd number, the player's overall score is zero. If the red die gives an even number, the player rolls it again and again until it is odd. The player's score is the sum of the two numbers, except for the previously mentioned case....

(ii) The other half the Black die is 2 4 or 6 (so has an average of 4), the White die will eventually be 1 3 or 5 (so has an average of 3); so the average total of a non-zero score is 7.

(iii) The average of 0 and 7 is 3.5; so that is the average score.

The picture shows a subway map.

If it takes 3 minutes to travel from one station to the next station and 3 minutes to change lines, what is the minimum time required to go from A to B?