Math Puzzles (Read the Rules!)

[veganray]

Once lined up, they must not communicate amongst themselves.

To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.

Your solution would involve a form of communication (though tacit), and is specifically prohibited. Frank would figger it out in a second, and slay them all.

[pdorries]

hrm, i guess since theres no extra communication involved there is a mathematical forumula involved, in which case I should stop thinking about this, im an accountant, I can handle rules and debits and credits, but throw in some advanced forumulas and I'm just gonna have to watch from the crowd... I will be checking up on this though, very curious to see the answer

[Trey133]

Alright...

Lets go Virgins!

Providing that they can discuss a non cheating strategy beforehand, this strategy should work. It will save 99 of them, and the first person is 50/50. Their strategy will be this. The first girl will count the number of blue hats, if that number is even she will guess that her hat is blue. This triggers all of the other girls to know that there are an even number of blue hats in the bunch. If the number of blue hats is odd, she will guess red. This triggers all of the other girls to know that there are an odd number of blue hats in the bunch. The next girl will now count the number of hats in front of her, if she counts an even number of blue hats in front of her, then she does not have a blue hat, and she will select red. The next girl will now count the number of hats in front of her, if she counts an odd number of blue hats in front of her, then she knows that she was the even blue hat, and will guess her hat as blue.

Haha, frank only gets to murderkill 1 virgin... but only has a 50/50 chance.

[veganray]

Frank makes it clear that if anyone breaks the rules then all the virgins will die, then allows the unfortunate ladies to consult before lining them up.

I think you have it, but just haven't quite articulated the thought process each virgin uses.

The first virgin counts all the blue hats in front of her (call it q) and then answers, "Red," if the number is odd or "Blue," if the number is even. Each subsequent virgin keeps track of the number of blue hats known to have been saved from behind her (call it y), then counts the number of blue hats in front of her (call it z).

If q was even, and if y&z are either both even or are both odd, then the virgin would answer, "Red." Otherwise, the virgin would answer, "Blue."

If q was odd, and if y&z are either both even or are both odd, then the virgin would answer, "Blue." Otherwise, the virgin would answer, "Red."

You are correct that this approach guarantees the survival of 99 virgins, with a 50/50 chance of the survival of the 100th.

Well done, sir! I look forward to your next submission.

[J-Bolt]

Crap! I actually thought of this on the ride home. Stupid beltway.

It did remind me of a time I got beat by a 7th grader in this high school math competition I was in.

[pdorries]

nice job treybroham lincoln

[Trey133]

Thank-you thank-you!

I am looking through some of my college notes, I had a fun econ problem I want to make sure I get right before I post it, math and graph friendly.

[Trey133]

I can't find it yet, I'll have to just get lucky and answer another one down the road when I do. Here is an easy teaser for the morning crowd.

My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 140 years. Can you tell me my age in years?

[J-Bolt]

grandson x = 7, son y = 49, me z = 84

Three variable system.
x+y+z=140
365x=52y
12x=z

Choose your fav method to solve

*Edit* Mine was old fashioned substitution.

[Trey133]

perfecto!

[J-Bolt]

You are presented with ten bottles of Flintstones vitamins. Each bottle contains one hundred pills. You are told that nine bottles contain poisonous pills and one bottle contains normal Fred, Barney, Wilma, Betty, Bam-bam, Pebbles and Dino vitamins and minerals. The other difference is that the poisonous pills weigh 1.0g each, and the normal pills weigh 1.1g each.

You are presented with a digital postal scale that has enough battery for one weighing. (Not a pan scale)

Find the non-poisonous pills.

[veganray]

Number the bottles 1 thru 10.
Take 1 pill from bottle #1, 2 pills from bottle #2, 3 pills from bottle #3, etc., until you take 10 pills from bottle #10.
Collect all the pills you have removed & weigh the lot.
If the total weight is 55.1g, bottle #1 is OK.
If the total weight is 55.2g, bottle #2 is OK.
If the total weight is 55.3g, bottle #3 is OK.
If the total weight is 55.4g, bottle #4 is OK.
If the total weight is 55.5g, bottle #5 is OK.
If the total weight is 55.6g, bottle #6 is OK.
If the total weight is 55.7g, bottle #7 is OK.
If the total weight is 55.8g, bottle #8 is OK.
If the total weight is 55.9g, bottle #9 is OK.
If the total weight is 56.0g, bottle #10 is OK.

[J-Bolt]

Yabbadabbadoo!

[veganray]

I yield my next puzzle to Trey133, as his last one was merely a trivial teaser.

[Trey133]

I yield my next puzzle to Trey133, as his last one was merely a trivial teaser.

Thank you sir, i'm at work right now though. So no notes to look through, if anyone wants to post a question up feel free. I'll send a message when my question is ready