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

Gialmere
Gialmere
Joined: Nov 26, 2018
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June 29th, 2020 at 8:14:02 AM permalink


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?
Have you tried 22 tonight? I said 22.
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
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Gialmere
June 29th, 2020 at 8:37:52 AM permalink
Quote: Gialmere

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?



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)

Gialmere
Gialmere
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June 29th, 2020 at 8:54:07 AM permalink
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
--------------------------------

Voldemort: So I need to lie?

Pinocchio: Yup!
Have you tried 22 tonight? I said 22.
Gialmere
Gialmere
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July 1st, 2020 at 8:15:02 AM permalink


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?
Have you tried 22 tonight? I said 22.
unJon
unJon
Joined: Jul 1, 2018
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Gialmere
July 1st, 2020 at 9:44:03 AM permalink
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?



Iím 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 thatís right I get:

3.5
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Gialmere
Gialmere
Joined: Nov 26, 2018
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July 1st, 2020 at 10:08:35 AM permalink
Quote: unJon


Iím 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 thatís 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.
Have you tried 22 tonight? I said 22.
IAchance5
IAchance5
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Gialmere
July 1st, 2020 at 10:39:52 AM permalink
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!
Gialmere
Gialmere
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July 1st, 2020 at 11:38:49 AM permalink
There are six possible scores: 0, 3, 5, 7, 9, and 11.

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
Have you tried 22 tonight? I said 22.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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Gialmere
July 1st, 2020 at 11:44:20 AM permalink
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....

(i) Half the time the score is zero.
(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.
Gialmere
Gialmere
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July 1st, 2020 at 11:56:19 AM permalink
And, since I'm bored at work...



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?
Have you tried 22 tonight? I said 22.

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