Home » General Chat » Circular File » Puzzle thread Dec. 22
 Puzzle thread Dec. 22 |
Tue, 23 December 2003 00:26  |
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 Ron |
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(sorry its late)
Here are this week's puzzles. I'll wait 24 hours for answer submissions via Private Message.
If you get ANY 5 puzzles correct, you get one chance to become this week's Puzzle Master. If you get all 6 correct, you get two chances.
1. I am a number with the following properties:
If I am not a multiple of 4, then I am between 60 and 69.
If I am a multiple of 3, I am between 50 and 59.
If I am not a multiple of 6, I am between 70 and 79.
What number am I?
2. Right before the fifth race at Santa Anita, the word got out that one of three horses was going to win the race: Lightning Bolt, a 2 to 1 shot; Golden Honey, a 3-1 shot; or Matchmaker, a 4-1 shot.
Assuming that this tip is true, how much would you have to bet on each of the three horses to be assured of coming out with a $39 profit?
3. Dave is in a hurry as he approaches the airport escalator, but Frank is in an even bigger hurry. For every 2 steps Dave takes, Frank takes three. Altogether, Frank takes 25 steps before dismounting the escalator, while Dave takes 20. Both Frank and Dave step on every step. How many steps does the escalator have showing at any given time?
4. "How old are your three daughters?" Fred asked a friend one day.
"The product of their ages in 36," replied his friend.
"You are not giving me enough information," protested Fred.
"The sum of their ages is the age of your oldest son."
"I still need more information."
"All right, then. I can tell you that the oldest daughter, who is at least a year older than the other two, is a very fine pianist."
"Ah! Now I know how old your daughters are."
What are the ages of Fred's friend's daughters?
5. After the parrot says a number, Robinson multiplies its digits and Crusoe adds its digits. If the difference between the two results is between the answers, they celebrate.
For example, if the parrot says 75, Robinson multiplies 7x5=35, whil
...
Ron Miller
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| Re: Puzzle thread Dec. 22 |
Wed, 24 December 2003 10:56  |
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| Ron |
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6 people got at least 5 answers correct, 3 of those got all 6 correct. HiltonL, gible, Sotek, Mazda, LEit, Ashlyn
And this week's Puzzle Master is gible.
Here are the answers:
1. 76 (is multiple of 4 not between 60 and 69, so first is fine, isn't multiple of 3, so 2nd is fine, isn't multiple of 6 and between 70 and 79, so 3rd is fine)
2. Lightning Bolt's chances of winning is 1/3
Golden Honey has 1/4 chance of winning
Matchmaker has 1/5 chance of winning
We seek amounts A, B, C sunch that A + B + C + 39 = 3A = 4B = 5C
Therefore, B = (3/4)A and C = (3/5)A. Substituting gives (3/4)A + (3/5)A + 39 = 2A, so 39 = (13/20)A, so A = 60. Similarly, B = 45, and C = 36, so we must bet #60 on Lightning Bolt, $45 on Golden Honey, and $36 on Matchmaker
3. 50 steps visible on the escalator.
The escalator moves 3 stairs in the time that the men walk their respective rates.
Dave takes 10 time units to walk the distance,he walks 20 and the escalator moves 30.
Frank takes 8.333 time units to walk the distance, he walks 25 and the escalator moves 25.
4. Ages are 9, 2, 2
For a product of 36 there are 8 different possibilities.
Only 2 of those possibilities have the same sum (13), which is what the second clue refers to.
The other sum of 13 is 6, 6 and 1, but we are told the eldest is ot least a year older than the others, so it has to be 2, 2 and 9.
5. Lowest is 37; 21 - 10 = 11, which is between 21 and 10.
6. The equation is always true.
sin(x)
----- = 6
n
Drop the parenthesis:
sinx
---- = 6
n
cancel the n:
six = 6
Thread unlocked.
Ron Miller
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| Re: Puzzle thread Dec. 22 |
Wed, 24 December 2003 21:13 |
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All praise Ron's random selector program 
Thanx to Sotek for explaining to me how betting odds work.
Q3:
Assuming the escalator moves at E steps/sec and there are n steps showing at any given time.
Frank took 25 steps on the escalator, which means his stepping rate is 25 divided by (n-25)/E, the total time he spent on the escalator, giving 25E/(n-25).
Similarly, Dave took 20 steps, which means his step rate is 20E/(n-20).
since for every 2 steps Dave takes, Frank takes 3, this gives
3 x 20E/(n-20) = 2 x 25E/(n-25)
=> n = 50.
Thus it doesn't matter what E is.
Merry Christmas
[Updated on: Wed, 24 December 2003 22:47] Report message to a moderator
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