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        riddles >> medium >> ANSWERS TO MEDIUM PUZZLES -- Part 3
        
(Message started by: I.M._Smarter_Enyu on Jul 26^th, 2002, 9:44am)

Title: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by I.M._Smarter_Enyu on Jul 26^th, 2002, 9:44am

RELATIVELY MEDIUM -- Part 3

>> COLORED DISK SPIN SENSORS Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed? <<

Assuming that you could take readings whenever you wanted... 2 sensors, placed right next to each other.

>> WATER BUCKETS Using only a 5-gallon bucket and a 3-gallon bucket, put exactly four gallons of water in the 5-gallon bucket. (Assume you have an infinite supply of water. No measurement markings on the buckets.) <<

Fill the 3, pour the 3 into the 5, fill the 3, pour what you can of the 3 into the 5, 3 now has 1 gallon, empty the 5, pour the 1 gallon from the 3 to the 5, fill the 3, pour the 3 into the 5.

>> TWO-CHILD FAMILY I In a two-child family, one child is a boy. What is the probability that the other child is a girl? <<

This is a classic permutation/combination puzzle trap. There are 4 possibilities: B/B, B/G, G/B, G/G. Of the 3 that have one boy, 2 have the other one being a girl, so it's 2/3. This is a variation of the classic Monty Hall problem.

>> TWO-CHILD FAMILY II In a two-child family, the older child is a boy. What is the probability that the other child is a girl? <<

There are 4 possibilities (in young/old order): B/B, B/G, G/B, G/G. Of the 2 that have the boy older, 1 has the other one being a girl, so it's 1/2.

>> 2 = 1 "Proof" that 2 = 1:

a = b
a2 = ab
a2 - b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1 <<

Duh, can't divide by 0 between steps 4 and 5.

>> BRIDGE CROSSING Four people, A, B, C, and D, are on one side of a bridge, and they all want to cross the bridge. However, it's late at night, so you can't cross without a flashlight. They only have one flashlight. Also, the bridge is only strong enough to support the weight of two people at once. The four people all walk at different speeds: A takes 1 minute to cross the bridge, B takes 2 minutes, C takes 5 minutes, and D takes 10 minutes. When two people cross together, sharing the flashlight, they walk at the slower person's rate. How quickly can the four cross the bridge? <<

A+B go = 2 minutes,
A goes back w/flashlight = 1 minute
C+D go = 10 minutes
B goes back w/flashlight = 2 minutes
A+B go = 2 minutes

Total = 17 min.

The breakthrough here is to realize the most time-consuming ones need to go together.

>> PUNCTUATION II Add punctuation to the following phrase to make something gramatically and logically coherent:

i had had had tom had had had had had had had had the praise of the teacher <<

I had had "had." Tom had had "had had." "Had had" had had the praise of the teacher.

**** I.M. Smarter Enyu!!! ****

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Kenneth on Jul 26^th, 2002, 12:11pm

on 07/26/02 at 09:44:07, I.M._Smarter_Enyu wrote:

RELATIVELY MEDIUM -- Part 3

>> WATER BUCKETS Using only a 5-gallon bucket and a 3-gallon bucket, put exactly four gallons of water in the 5-gallon bucket. (Assume you have an infinite supply of water. No measurement markings on the buckets.) <<

Fill the 3, pour the 3 into the 5, fill the 3, pour what you can of the 3 into the 5, 3 now has 1 gallon, empty the 5, pour the 1 gallon from the 3 to the 5, fill the 3, pour the 3 into the 5.

There is an even easier way.

Fill the 5 and pour into the 3 (the 5 now has 2 gallons). Empty the three and pour in the remaining quantity of the 5 (2 gallons in the three gallon container). Fill the 5 and pour into the 3 gallon container (only 1 gallon can be poured into the 3 before it fills). Thus, 4 gallons remain in the 5 gallon containers. I believe this requires less steps.

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Anonymous on Jul 28^th, 2002, 10:51pm

No, the chance of the second child being a girl is 50/50.

the two choices are independent of each other. We know that the first child is a boy. Therefore the probability of the child being a boy is 1.

so there are only two posssible situations
1 boy 2 boy
1boy 2 girl

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Mike H. on Jul 31^st, 2002, 8:27am

No, the probability that the second child is a girl is 100%!
If there are two children and ONE (exactly one, not at least one) is a boy, then the other has to be a girl.

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Mike H. on Jul 31^st, 2002, 8:31am

Sorry, let me clarify, I was commenting on the first "two child" problem:

>> TWO-CHILD FAMILY I In a two-child family, one child is a boy. What is the probability that the other child is a girl? <<

This is a classic permutation/combination puzzle trap. There are 4 possibilities: B/B, B/G, G/B, G/G. Of the 3 that have one boy, 2 have the other one being a girl, so it's 2/3. This is a variation of the classic Monty Hall problem.

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Sean Davis on Aug 26^th, 2002, 3:06pm

As to the bridge crossing riddle, I'm convinced the correct answer is 19 minutes, not 17.

A + D cross the bridge = 10 minutes
A comes back = 1 minute
A + C cross the bridge = 5 minutes
A comes back = 1 minute
A + B cross the bridge = 2 minutes

10 + 1 + 5 + 1 + 2 = 19 minutes total. :-*

Title: Re: ANSWERS TO MEDIUM PUZZLES -- Part 3
Post by Sean on Aug 26^th, 2002, 3:09pm

damn... should have read your answer more carefully. Guess I'm wrong. :D