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Puzzle thread Jan. 6

Tue, 06 January 2004 22:20

Ron

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Sorry that these are late by a day.

Here are this week's puzzles. 24hour timelimit, PM me your answers. 5 correct answers give you 1 chance at being chosen as the Puzzle Master. 6 correct answers give you 2 chances.

1. An enormous military band was marching and playing at an official ceremony. At the beginning, the musicians formed a perfect square; that is, there were the same number of rows and columns. Suddenly, they changed formation and became a rectangle in which the number of columns of musicians was greater by 5 than it had been in the previous formation.
How many musicians were there in the band?

2. In a school there are 158 students. Although there are more girls than boys, only 1/11 of the girls wear glasses, while 1/7 of the boys wear them.
How many boys and how many girls are there in the school?

3. What 5 numbers must be placed in the 5 blanks at the base of this pyramid so that, if in each of the remaining 10 circles is placed the sum of the 2 circles immediately below it, the result is a pyramid of 15 different numbers with the number 97 at the top?

    97
   o  o
  o  o  o
 o  o  o  o
o  o  o  o  o

4. "Inversion"
The numbers from 1 to 10 are arranged according to strict and unusual criteria. What's the secret to this sequence?
3,9,1,5,10,7,2,4,8,6

5. Use the numbers 1 to 9 to replace each x below, use each number only once, get a correct numerical operation.
SQUAREROOT(xxx)=x+x+x+x+x+x

6. (cultural puzzle, American dates used) On his first voyage, the astronaut was in orbit from 6:34 on May 8 until 1:02 on July 9, a total of 61 days, 19 hours, and 28 minutes.
"How strange," he said upon returning to Earth. "The first date is written 5/8, 6:34, and the second, 7/9, 1:02. Those two dates use all the numbers between 0 and 9, each only once."
The second trip had the same outrageous characteristic: the departure and return dates, both during the same year, were written using all the numbers 0 to 9 only once. But ...

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[Updated on: Tue, 06 January 2004 22:23]

Ron Miller
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Re: Puzzle thread Jan. 6

Wed, 07 January 2004 23:21

Ron

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Looks like I picked easy ones again. 6 people got at least 5 puzzles correct. 3 of them got all 6 correct.

HiltonL, Sotek, Mazda, Ashlyn, overworked, Leit

The RNG picks Ashlyn. (honest guys, it *is* random, I've checked, so I'm not biased towards Ashlyn)

Here are the answers:

1. Suppose in the square formation the number of musicians was n^2. If it was possible for them to change their formation to that of a rectangle with n+5 columns, that means that n+5 divides n^2. Since n^2 = (n+5)(n-5)+25, this means that n+5 divides 25. THe only divisor of 25 greater than 5 is 25 itself, so n+5=25 and n=20. The number of musicians in the band, therefore, was 400.

2. There are only 2 ways of expressing the number 158 as the sum of a multiple of 7 and a multiple of 11: 147+11 and 70+88. Since there were more girls than boys, the number of boys must therefore be 70 while the number of girls must be 88.

3. Many possible answers (I really should have checked this one first).

4. They are arranged alphabetically when read (spelled) backwards

5. sqrt(729) = 1 + 3 + 4 + 5 + 6 + 8

6. 2nd voyage, longest possible, was between Jan. 2 at 0:34 and Sept. 8 at 7:56 (250 days, 7 hours, 22 minutes, in a leap year)
3rd voyage, shortest possible, was between Feb. 9 at 8:57 and March 1 at 0:46 (19 days, 15 hours, 49 minutes, non-leap year)

Thread unlocked.

Ron Miller
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Re: Puzzle thread Jan. 6

Thu, 08 January 2004 01:50

nash

Chief Petty Officer

Messages: 84
Registered: December 2003
Location: Sydney Australia

Ron wrote on Wed, 07 January 2004 14:20

1. An enormous military band was marching and playing at an official ceremony. At the beginning, the musicians formed a perfect square; that is, there were the same number of rows and columns. Suddenly, they changed formation and became a rectangle in which the number of columns of musicians was greater by 5 than it had been in the previous formation.
How many musicians were there in the band?

Damn, misread this as the new number of columns is 5 larger then the new number of rows... ie (n^2) = m * m - 5.

Sentio aliquos togatos contra me conspirare.

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Re: Puzzle thread Jan. 6

Thu, 08 January 2004 02:10

HiltonL

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Ron wrote on Thu, 08 January 2004 06:21

Congratulations Ashlyn (again)! Shocked

The space-trip one has to win the award for most entertaining puzzle this week - very good Ron...

Cheers
Hilton

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Re: Puzzle thread Jan. 6

Thu, 08 January 2004 05:34

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

Congrats Ashlyn again. Cool

*mazda looks for a pattern in the award of Master *
Looks like it's biased alphabetically.
Proportional to (1/n squared) where n is your order in the list alphabetically.
Poor Sotek has no chance !

Liked the proof for number 1. Very elegant.
Whoever came up with that deserves to win.

I had a much more complicated method that basically showed that the other side in the rectangle must be a multiple of 16.
Fortunately I didn't tell it to Ron ! Laughing

However it was lacking as it didn't prove there was only one solution.

Another way is to consider the 4 equations
x squared = (x+5)(x-5+n) where n = 1 to 4
These give x = 20, 7.5, 3.33, 1.25.
But still not elegant.

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Re: Puzzle thread Jan. 6

Thu, 08 January 2004 08:06

True-Chaos

Crewman 1st Class

Messages: 26
Registered: October 2003
Location: Canada

Too easy? bah!
Cool

I never would have gotten number 4, and was too lazy to brute force the last one Very Happy

~The World be black and white except for the shades of gray~

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Re: Puzzle thread Jan. 6

Thu, 08 January 2004 10:26

mazda

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Location: Reading, UK

The last one was definitely *not* brute force.

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Re: Puzzle thread Jan. 6

Mon, 12 January 2004 03:22

HiltonL

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Past Weekly Puzzle Master

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mazda wrote on Thu, 08 January 2004 17:26

The last one was definitely *not* brute force.

Funny you should mention that, because I solved it pen-and-paper in about 5 minutes, and then another 2 minutes after I remembered that February was the shortest month... Embarassed

Then, because I had nothing to do at work, I brute-forced it as well, just to make sure I hadn't missed a trick. I was so pleased when my program spat out the same answers as my pen-and-paper work. Very Happy

When you're forced to write VB6 and ASP all day, writing a little routine in C# to solve a puzzle is such a treat, I *HOPE* each week that one or two puzzles lend themselves to brute-force.

Cheers
Hilton

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