 Puzzle thread Oct. 27 |
Mon, 27 October 2003 14:33  |
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 Ron |
 | Commander
Forum Administrator
Stars! AutoHost Administrator |
Messages: 1231
Registered: October 2002
Location: Collegedale, TN | |
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1. Find the 8-digit number:
The first 2 digits for a number that is half the number formed by the third and fourth digits. The fourth is one-third the number formed by the fifth and sixth digits, and the sixth is one-fourth of the number formed by the seventh and eighth digits.
The answer I'm looking for does not contain any zeros. Find all valid answers. Example, first 4 digits '1224', 12 is half of 24.
2. A customer brought four items to the cashier of the 7-11 convenience store. "That will be $7.11," the cashier said. At first the customer thought it was a joke. "Ha, ha. Seven-eleven. I get it." But the clerk was serious. "No, really. I multiplied the prices of the four items you gave me, and I came up with $7.11."
"You multiplied them?" the customer asked. "You're supposed to add them, you know."
"I know," said the clerk, "but it doesn't make any difference if I add or multiply. The total is still $7.11."
What were the prices of the four items?
I will wait 24 hours for people to PM me the correct answers, and I will then use a random number generator to pick one of them to have 'Weekly Puzzle Master' custom avatar diplayed under their name for a week.
Naturally, you won't want to share answers until the I announce the winner. 
This thread will be locked until a winner is selected.
[Updated on: Mon, 27 October 2003 21:04]
Ron Miller
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 Re: Puzzle thread Oct. 27 |
Tue, 28 October 2003 16:26  |
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| Ron |
| Commander
Forum Administrator
Stars! AutoHost Administrator |
Messages: 1231
Registered: October 2002
Location: Collegedale, TN | |
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The 5 people who sent in the correct answers were:
LEit, Mazda, Freakyboy, Ashlyn, and BlueTurbit.
I assigned each person a number, in order, from 1 to 5 and using the following PERL program:
#!/usr/bin/perl
srand(time() ^ ($$ + ($$ << 15)));
$number = $ARGV[0];
if(!$number){
print "Usage: rand [maxnumber]\n rand.pl returns a random number between 1 and [maxnumber]\n";
exit;
}
$number = int($number);
$rand = int(rand $number) + 1;
print "Random number between 1 and $number = $rand\n";
The person randomly drawn to be this week's 'Puzzle Master' is Ashlyn 
She has been given a custom tag and avatar for the week.
Several people mentioned that they used a spreadsheet or wrote a program to solve the puzzles. Since I didn't specify one way or the other, its fine. I wouldn't be able to verify that someone didn't use a computer program anyway.
Next week's puzzles will probably be a bit harder, and not so easily solved with a computer.
The answers to this weeks puzzles were:
13261832
14282416
18361832
19382416
23461832
24482416
28561832
29582416
33661832
34682416
38761832
39782416
43861832
44882416
48961832
49982416
and
$1.20 $1.25 $1.50 $3.16
Thread unlocked for comments.
[Updated on: Tue, 04 November 2003 17:45]
Ron Miller
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| Re: Puzzle thread Oct. 27 |
Wed, 29 October 2003 11:10 |
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| LEit |
 | Lt. Commander |
Messages: 879
Registered: April 2003
Location: CT | |
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The program that solved it (not a very brilliant program, mostly brute force):
int mulmon(int a, int b, int c, int d)
{
int r = a * b * c * d;
if (r % 1000000 != 0) return 0;
r /= 1000000;
return r;
}
int main(int argc, char* argv[])
{
int i = 708, j = 1, k = 1, l = 1;
for (i = 1; i < 700; ++i)
for (j = 1; j < 700; ++j)
for (k = 1; k < 700; ++k)
{
l = 711 - i - j - k;
if (l > 0 && mulmon(i, j, k, l) == 711)
printf("Result %d %d %d %d\n", i, j, k, l);
}
return 0;
}
This found 24 answers (the 4 prices in all possible orders...)
- LEitReport message to a moderator
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| Re: Puzzle thread Oct. 27 |
Thu, 30 October 2003 06:22 |
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| mazda |
 | Lieutenant |
Messages: 655
Registered: April 2003
Location: Reading, UK | |
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The 7-11 one I solved by factorising 711 and noticing a large prime - 79.
So one of the amounts had to be a multiple of 0.79 (9x0.79=7.11).
Then I simply tried each multiple of 0.79 and wrote down what it left as the sum and product of the other 3 terms.
Then I used trial and error.
Now we are trying to get a product which is a whole number of pounds and we are using prices fixed to 2 d.p.
This means we can't use fractions like 1/3, we would have to use 0.33 which when multiplied by 3 is 0.99 not 1.00.
So anything ending in 5's or 10's would look good and anything else wouldn't.(note that if we were using an infinite number of places rather than monetary amounts then this wouldn't matter, there would be a lot more solutions, each one based on considering all multiples of all different factors of 711).
In the case of a single multiple of 0.79 we are left with 6.32 to spend. This doesn't look very promising. No way are we going to get a product of 9 out of something adding up to 6.32.
Not in monetary amounts anyway.
A little intuition and inspection leads us to 4 x 0.79 = 3.16
This leaves us needing a sum of 3.95 and a product of 2.25.
For this case you can eliminate any amount being 1.00 or less (to get 2.25 we would need 1.5, 1.5, 1.00 which adds to 4 and we only have 3.95 left to spend) so all 3 amounts have to be more than 1.00.
Simply a guess of 1.25, leaves us needing a product of 1.8 with 2.70 to spend. 1.8 = 1.50 x 1.20.
Hence the 4 amounts - 3.16, 1.25, 1.50 and 1.20.
This is an odd problem in that we are restricting values to not only rational numbers, but to values that are a whole number of hundredth's.
I wonder if this is the only rational solution to the probblem - i.e. if we allow fractions like 4/3 or 27/17 into the realm of possible solutions then are there any more ?
Or do we have to go to irrational numbers where I've already indicated there will be solutions.
M
...
I am the God of hell fire, and I bring you
... Brian PithersReport message to a moderator
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| Re: Puzzle thread Oct. 27 |
Fri, 31 October 2003 15:41 |
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| LEit |
| Lt. Commander |
Messages: 879
Registered: April 2003
Location: CT | |
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Here's a puzzle for those of you who cannot wait:
STARS
SUPER
+NOVA
-----
VAPOR
Each letter is a digit, each digit only applies to one letter.
The letters T,U, and N are interchangable. So are E and R.
There are two solutions that I found, not counting swapping TUN or ER.
PM me with your answers, however, the prize is a copy of FreeStars (when that is no longer vapor either...)
- LEitReport message to a moderator
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