Well done again, you two! Its now really hard to find/make up problems...

Answers:
13. 18 Miles (Correct Answer by: William Rothamel)
14. 3 Spheres (Correct Answer by: Mr. Kevvy)

Question 15 is wrong, Mr. Kevvy. Try Again!!!!

Standings so far:
1. Mr. Kevvy - 4 1/2 Points
2. WinterKnight - 4 Points
3. William Rothamel - 3 1/2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

Q15 is still up for grabs....

---

- Luke.

I'm guessing 128 but I will go back and try to devise a mixing and numbering strategy strategy to allow perhaps very few tests. I assume that the test cannot detect differing levels of poison concentrations and distinguish among them ? ne pas ?

regards,


DADDIO

Sorry mate, but you have the wrong answer!!!....

Also, what you get in the question is what you are given.... I cannot answer your question...

Luke.

---

- Luke.

Today, I was notified about a possible correct answer... that I deemed to be incorrect.....

15. HARD -The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desires only to minimize the maximum possible tests required to determine which exact glass was poisoned. The mathematician started by asking a detective to select a single glass at random for testing. "Wouldn't that waste a test?", the detective asked. "No, besides I'm in a gambling mood.", the mathematician replied. How many glasses were there?



I go with 129 glasses. 128 is a power of 2, and he wants the group to be an even power of two for elimination-by-halves testing, so the 129th is the odd one out.

Mr. Kevvy's Answer to Q15 is correct....
Q15 Answer: 129 glasses....

I credit Mr. Kevvy the full point for the question.... and a half point for the inconvenience....

Standings so far:
1. Mr. Kevvy - 6 Points
2. WinterKnight - 4 Points
3. William Rothamel - 3 1/2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

Sorry for all inconvenience...
More Problems coming soon.......

Best Regards,
Luke.

---

- Luke.

The binary numbers 129 thru 200 all have only a 1 in the 8th column. 129 is the lowest number but the others seem possible as well. Assuming a binary mix of the glasses into 8 pails. The eighth pail would have a unique glass in it for any number of glasses in the range 129-200. Hence you could taste that last glass and avoid testing the other seven pails if it turned out to test positive for poison.
Regards,

Daddio

OK, here are two more questions to finish off my day.....

16. EASY (WORTH 1 POINT) - An urn contains a number of colored balls, with equal numbers of each color. Adding 20 balls of a new color to the urn would not change the probability of drawing (without replacement) two balls of the same color.
How many balls are in the urn? (Before the extra balls are added.)

(Mr. Kevvy and William Rothamel may NOT answer the above (No. 16) question....)


17. HARD (WORTH 1 POINT) A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.)

What is the probability that the total value is divisible by 13?


Have a go and best regards,
Luke.

---

- Luke.

17. A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down. The total value of the cards which landed face up is then calculated. (Card values are assigned as follows: Ace=1, 2=2, ... , 10=10, Jack=11, Queen=12, King=13. There are no jokers.) What is the probability that the total value is divisible by 13?

It's equally probable that the cards land face up or face down, so that doesn't change the outcome, and there's an equal distribution of all the values (as opposed to card games such as cribbage where all the face cards are worth 10, or having more of one value card than another, etc.) So I'll go with the simple answer: 1 in 13, or 13 to 1. I can't see how it could be otherwise.

---

Umm....HINT: I'm sorta looking for a decimal figure....
So I'll have to say that's incorrect....

---

- Luke.

Umm.... I'm sorta looking for a decimal figure....
SO I'll have to say that's incorrect....

OK... 1 in 13 is 0.0(769230)
(just 1 divided by 13.)

---

Umm.... I'm sorta looking for a decimal figure....
SO I'll have to say that's incorrect....

OK... 1 in 13 is 0.0(769230)
(just 1 divided by 13.)

Ummmm.... My book says that this questions' is supposed to be hard....
That is the first and last time I'm using that book....

By any chance, were you using a calculator?

Official Answer Question 17: 0.076923

Standings:
1. Mr. Kevvy - 7 Points
2. WinterKnight - 4 Points
3. William Rothamel - 3 1/2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

Best Regards,
Luke

PS (@ everybody except for Mr. Kevvy & William Rothamel, question 16 is still up for grabs...)

---

- Luke.

By any chance, were you using a calculator?

Yes, for the division. Did we have to use pencil and paper for the arithmetic? ;^)

---

No answers today, just dropped in to post this link Mental workout 'boosts the brain'.

No answers today, just dropped in to post this link Mental workout 'boosts the brain'.

Good link... and exactly why I'm here: keep brain from turning into mush.

---

Great link WinterKnight!
I get my brain exercises from my daily Sudoku......

@Mr. Kevvy, I would like people to try and use pencil + paper.... but there is no way of knowing if people do it with a calculator....
So using a calculator is discouraged but not breaking any rules.....

BTW.....How again do you change the title of a thread? I've had a idea....

Luke.

---

- Luke.

Great link WinterKnight!
@Mr. Kevvy, I would like people to try and use pencil + paper.... but there is no way of knowing if people do it with a calculator....
So using a calculator is discouraged but not breaking any rules.....

Geez, I wrote a Python script for # 10. :^)

---

Scripts in Python are hereby allowed.....

---

- Luke.

Great link WinterKnight!
I get my brain exercises from my daily Sudoku......

@Mr. Kevvy, I would like people to try and use pencil + paper.... but there is no way of knowing if people do it with a calculator....
So using a calculator is discouraged but not breaking any rules.....

BTW.....How again do you change the title of a thread? I've had a idea....

Luke.

Edit a post, I think.
Going now, 'nother meeting, only thing changed is, heads of h/ware and s/ware hate each other more and become more entrenched in their beliefs.
I hinted at problem, with suggested solution 18 months ago, both poo-pooed the idea. Now its come back and bit their ______.

Thanks WinterKnight.... lets see if this works....

Hope the meeting goes well....

*Yuss*.... It worked....

---

- Luke.

Howdy,

Calculators and interpreters (BASIC etc) are usually found on everyones computer; or can be easily added. In the old days when I was teaching BASIC (I even spoke with John Kemeny once) I found that a simulation ( random numbers or straight iteration) was often the easiest way to a solution. .

Luke should decide if that's OK by his rules. Since answers here are often required to several decimal places then calculators should be the order of the Day.

Others (such as me) may want to look up the solution to an integral that they have long forgotten. I guess I am in favor of using the computer to any advantage--even though it may access information compiled by others--kind of like the way of the world now.

kind of an interesting question for this thread--

What do you think luke, Kevvy, others ,,,??

best regards,

Bill
AKA DADDIO

Great link WinterKnight!
I get my brain exercises from my daily Sudoku......

@Mr. Kevvy, I would like people to try and use pencil + paper.... but there is no way of knowing if people do it with a calculator....
So using a calculator is discouraged but not breaking any rules.....

BTW.....How again do you change the title of a thread? I've had a idea....

Luke.

Edit a post, I think.
Going now, 'nother meeting, only thing changed is, heads of h/ware and s/ware hate each other more and become more entrenched in their beliefs.
I hinted at problem, with suggested solution 18 months ago, both poo-pooed the idea. Now its come back and bit their ______.

I hope you poo-pooed their poo-poos! Because you must not make the mistake of ignoring their poo-poos!

---

ITI SAPIS
POTANDA
TINONE