Home » General Chat » Circular File » Puzzle Thread Aug. 10
 Puzzle Thread Aug. 10 |
Tue, 10 August 2004 22:51  |
|
 Ron |
 | Commander
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Messages: 1231
Registered: October 2002
Location: Collegedale, TN | |
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Here is a weekly puzzle thread (long overdue, but don't expect them to continue *every* week)
You have 24 hours to PM me the answers.
Answer any 5 questions correctly to get one chance to win, or answer all 6 questions for 2 chances to win.
Winner will become this week's Puzzle Master.
1.
----- ----- -----
| B | | A | | K |
| H | is to | F | as | L | is to:
| T | | R | | M |
----- ----- -----
a.
-----
| M |
| J |
| L |
-----
b.
-----
| J |
| K |
| J |
-----
c.
-----
| I |
| K |
| J |
-----
d.
-----
| J |
| J |
| K |
-----
2. Which is the odd one out, and why?
a.
\
o o
@
---
b.
/
o @
o
---
c.
|
o o
o
---
d.
\
o o
@
---
e.
/
@ o
o
---
f.
/
o o
@
---
g.
/
o @
o
---
h.
/
@ o
o
---
i.
\
o o
@
---
j.
/
o @
o
---
k.
\
o o
@
---
l.
|
o o
o
---
3. Suppose you have two candles of the same height but of different widths. One takes 4 hours to burn all the way down, while the other takes 7 hours. Assuming both candles burn down at steady rates, how long will it take before one candle is twice as tall as the other? (give the answer in hours:minutes, and show how you got the answer)
4. What is the smallest solution, in whole numbers (integers) only, to the equation below? (what is the smallest values for x, y, and z that solve equation?)
1 1 1
--- + --- = ---
x^2 y^2 z^2
5. The square below (marked with X's) fits exactly in the triangle shown.
The triangle vertices coordinates are marked. The top two vertices of the square exactly touch the sides of the triangle.
What is the length of one of the squares sides? Show how you got the answer.
| (4,4)
| /--
| / \
| / --
| /------- \
| / |xxxxx| --
| / |xxxxx| \
| / |xxxxx| --
|/ |xxxxx| \
|-------------------------------------
(0,0) (10,0)
6. Find 5 distinct integers A, B, C, D, and E, each less than 10, so that the following equation is true?
...
[Updated on: Tue, 10 August 2004 22:52]
Ron Miller
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| Re: Puzzle Thread Aug. 10 |
Wed, 11 August 2004 22:49  |
|
| Ron |
| Commander
Forum Administrator
Stars! AutoHost Administrator |
Messages: 1231
Registered: October 2002
Location: Collegedale, TN | |
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They must have been too easy this time. Out of the 6 people that participated, 5 got all 6 puzzles correct.
LEit, wizard, overworked, Kotk, and HiltonL got all 6 puzzles correct. The RNG chose overworked as this weeks Puzzle Master.
1. d
2. f
3. The fraction of candle A that remains after 't' hours is (4-t)/4 and the fraction of candle B that remains is (7-t)/7. We want to find the point at which the slower-burning candle is twice as tall as the faster-burning candle. This happens when 2((4-t)/4) = (7-t)/7 so 28-7t=14-2t which gives us that 5t=14 or t=2.8 hours. This is 2 hours and 48 minutes.
4. Pythagoras The smallest solution is x (or y) = 15, y (or x) = 20,and z=12.
5. The equation of the upward sloping line is simply y=x, while the equation of the downward sloping line is given by y=-(2/3)(x-10), or simply 2x+3y=20. The upper-left corner of the square is on the line y=x, so its coordinates are (n,n), where 'n' is the length of a side of the square. The coordinates of the upper-right corner are then 2(2n)+3n=20, or 7n=20. Therefore the length of the square equals 20/7.
6. The book answer is A=2, B=4, C=5, D=6, and E=9. However several other answers were submitted that are also valid. 0, 2, 3, 6, 7 and 5, 3, 1, -1, 6
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Ron Miller
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| Re: Puzzle Thread Aug. 10 |
Thu, 12 August 2004 06:50 |
|
| mazda |
 | Lieutenant |
Messages: 655
Registered: April 2003
Location: Reading, UK | |
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| Ron wrote on Thu, 12 August 2004 03:49 |
LEit, wizard, overworked, Kotk, and HiltonL got all 6 puzzles correct.
|
I assume I was the odd one out and only got 5. 
| Quote: |
6. The book answer is A=2, B=4, C=5, D=6, and E=9. However several other answers were submitted that are also valid. 0, 2, 3, 6, 7
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Weak, but passable. | Quote: |
and 5, 3, 1, -1, 6
|
Very weak. That's a "I can't find the right answer, so I'll put this one instead".
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| Re: Puzzle Thread Aug. 10 |
Thu, 12 August 2004 10:29 |
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| mazda |
| Lieutenant |
Messages: 655
Registered: April 2003
Location: Reading, UK | |
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Aha.
Deliberately looking for a different answer becuase the question isn't *quite* specific enough is definitely allowed.
Especially when the required answer is just a matter of simple effort.
I tried something else for 2) as well.
I converted each different face into a single letter (A, B etc) and tried to see if there was an expanding pattern.
I also briefly wondered whether they were the "notes" to a familiar tune !
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I sent her a PM, asking if they were so easy that she felt them beneath her 
