wu :: forums
wu :: forums - Mosquitoes and new repellent

Welcome, Guest. Please Login or Register.
Jan 24th, 2022, 9:44pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: william wu, Grimbal, SMQ, towr, Icarus, ThudnBlunder, Eigenray)
   Mosquitoes and new repellent
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Mosquitoes and new repellent  (Read 4876 times)
Altamira_64
Junior Member
**





   


Posts: 116
Mosquitoes and new repellent  
« on: Jun 15th, 2012, 12:15am »
Quote Quote Modify Modify


A team of biologists has been working on a new repellent to face the increasing number of mosquitoes in an area of Africa. They have been working with the combination of various substances in different percentages and each sample was placed in a test tube and then tested on a mosquito. They then waited for one hour to see if the mosquito would die. All test tubes with the various repellent samples were kept aside, just in case they were needed again. The first 499 attempts and absolutely no effect on the mosquito but the 500th killed it after about one hour. They started jumping of joy and dancing for their success. Unfortunately, in the meantime, a careless assistant mixed up the test tubes, so in effect they did not know which one had the correct fluid. Moreover, there were only 10 mosquitoes left and also the deadline for the end of the experiment was in 1,5 hour. Given that they would need about half an hour to prepare a new experiment, how can they determine which test-tube contains the correct sample, within the remaining one hour?
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Mosquitoes and new repellent  
« Reply #1 on: Jun 15th, 2012, 12:25am »
Quote Quote Modify Modify

Sound like the criminal cupbearer riddle (forum thread).
« Last Edit: Jun 15th, 2012, 12:26am by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Grimbal
wu::riddles Moderator
Uberpuzzler
*****






   


Gender: male
Posts: 7517
Re: Mosquitoes and new repellent  
« Reply #2 on: Jun 15th, 2012, 4:22pm »
Quote Quote Modify Modify

If there are only 10 mosquitoes left, just kill them and you won't need the repellent any more.  Roll Eyes
IP Logged
Altamira_64
Junior Member
**





   


Posts: 116
Re: Mosquitoes and new repellent  
« Reply #3 on: Jun 16th, 2012, 12:22am »
Quote Quote Modify Modify

So let's start by saying that we divide the tubes in groups of 2 4 8 16 32 64 128 and the remaining 246. We start by giving each mosquito one drop from every tube in each group and wait for one hour to see the results. Then what?
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Mosquitoes and new repellent  
« Reply #4 on: Jun 16th, 2012, 2:13am »
Quote Quote Modify Modify

Assign each vial a binary number, and each mosquito a bit in the binary number.
Give each mosquito a drop from each vial where its bit is one.
The live and dead mosquitoes after one hour spell the binary number of the correct vial.
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Altamira_64
Junior Member
**





   


Posts: 116
Re: Mosquitoes and new repellent  
« Reply #5 on: Jun 16th, 2012, 3:40am »
Quote Quote Modify Modify

Wow!  
So, to start with, here is the list of the 500 vials in binary format:
000000001
000000010
000000011
000000100
000000101
000000110
000000111
000001000
000001001
000001010
000001011
000001100
000001101
000001110
000001111
000010000
000010001
000010010
000010011
000010100
000010101
000010110
000010111
000011000
000011001
000011010
000011011
000011100
000011101
000011110
000011111
000100000
000100001
000100010
000100011
000100100
000100101
000100110
000100111
000101000
000101001
000101010
000101011
000101100
000101101
000101110
000101111
000110000
000110001
000110010
000110011
000110100
000110101
000110110
000110111
000111000
000111001
000111010
000111011
000111100
000111101
000111110
000111111
001000000
001000001
001000010
001000011
001000100
001000101
001000110
001000111
001001000
001001001
001001010
001001011
001001100
001001101
001001110
001001111
001010000
001010001
001010010
001010011
001010100
001010101
001010110
001010111
001011000
001011001
001011010
001011011
001011100
001011101
001011110
001011111
001100000
001100001
001100010
001100011
001100100
001100101
001100110
001100111
001101000
001101001
001101010
001101011
001101100
001101101
001101110
001101111
001110000
001110001
001110010
001110011
001110100
001110101
001110110
001110111
001111000
001111001
001111010
001111011
001111100
001111101
001111110
001111111
010000000
010000001
010000010
010000011
010000100
010000101
010000110
010000111
010001000
010001001
010001010
010001011
010001100
010001101
010001110
010001111
010010000
010010001
010010010
010010011
010010100
010010101
010010110
010010111
010011000
010011001
010011010
010011011
010011100
010011101
010011110
010011111
010100000
010100001
010100010
010100011
010100100
010100101
010100110
010100111
010101000
010101001
010101010
010101011
010101100
010101101
010101110
010101111
010110000
010110001
010110010
010110011
010110100
010110101
010110110
010110111
010111000
010111001
010111010
010111011
010111100
010111101
010111110
010111111
011000000
011000001
011000010
011000011
011000100
011000101
011000110
011000111
011001000
011001001
011001010
011001011
011001100
011001101
011001110
011001111
011010000
011010001
011010010
011010011
011010100
011010101
011010110
011010111
011011000
011011001
011011010
011011011
011011100
011011101
011011110
011011111
011100000
011100001
011100010
011100011
011100100
011100101
011100110
011100111
011101000
011101001
011101010
011101011
011101100
011101101
011101110
011101111
011110000
011110001
011110010
011110011
011110100
011110101
011110110
011110111
011111000
011111001
011111010
011111011
011111100
011111101
011111110
011111111
100000000
100000001
100000010
100000011
100000100
100000101
100000110
100000111
100001000
100001001
100001010
100001011
100001100
100001101
100001110
100001111
100010000
100010001
100010010
100010011
100010100
100010101
100010110
100010111
100011000
100011001
100011010
100011011
100011100
100011101
100011110
100011111
100100000
100100001
100100010
100100011
100100100
100100101
100100110
100100111
100101000
100101001
100101010
100101011
100101100
100101101
100101110
100101111
100110000
100110001
100110010
100110011
100110100
100110101
100110110
100110111
100111000
100111001
100111010
100111011
100111100
100111101
100111110
100111111
101000000
101000001
101000010
101000011
101000100
101000101
101000110
101000111
101001000
101001001
101001010
101001011
101001100
101001101
101001110
101001111
101010000
101010001
101010010
101010011
101010100
101010101
101010110
101010111
101011000
101011001
101011010
101011011
101011100
101011101
101011110
101011111
101100000
101100001
101100010
101100011
101100100
101100101
101100110
101100111
101101000
101101001
101101010
101101011
101101100
101101101
101101110
101101111
101110000
101110001
101110010
101110011
101110100
101110101
101110110
101110111
101111000
101111001
101111010
101111011
101111100
101111101
101111110
101111111
110000000
110000001
110000010
110000011
110000100
110000101
110000110
110000111
110001000
110001001
110001010
110001011
110001100
110001101
110001110
110001111
110010000
110010001
110010010
110010011
110010100
110010101
110010110
110010111
110011000
110011001
110011010
110011011
110011100
110011101
110011110
110011111
110100000
110100001
110100010
110100011
110100100
110100101
110100110
110100111
110101000
110101001
110101010
110101011
110101100
110101101
110101110
110101111
110110000
110110001
110110010
110110011
110110100
110110101
110110110
110110111
110111000
110111001
110111010
110111011
110111100
110111101
110111110
110111111
111000000
111000001
111000010
111000011
111000100
111000101
111000110
111000111
111001000
111001001
111001010
111001011
111001100
111001101
111001110
111001111
111010000
111010001
111010010
111010011
111010100
111010101
111010110
111010111
111011000
111011001
111011010
111011011
111011100
111011101
111011110
111011111
111100000
111100001
111100010
111100011
111100100
111100101
111100110
111100111
111101000
111101001
111101010
111101011
111101100
111101101
111101110
111101111
111110000
111110001
111110010
111110011
111110100
 
So you are saying that I assign the first bit to mosquito number 1, the second to number 2 etc, so in effect I give mosquito number 1 one drop from vials 1, 3, 5, 7 etc, mosquito number 2 one drop from 2, 3, 6, 7, 10, 11 etc and so on.  
 
Then, if, for example, the correct repellent is in vial 27, the mosquitoes 1, 2, 4 and 5 will die. Is this it?
So we also have one extra mosquito as bonus gift!
(because we only need 9 for this method).
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Mosquitoes and new repellent  
« Reply #6 on: Jun 16th, 2012, 4:11am »
Quote Quote Modify Modify

Yup, that's it.
 
You could use the final mosquito to check for errors, using it as a parity bit Tongue (With a few more you could do an error-correcting code.)
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Altamira_64
Junior Member
**





   


Posts: 116
Re: Mosquitoes and new repellent  
« Reply #7 on: Jun 17th, 2012, 1:52am »
Quote Quote Modify Modify

Thanks for the assistance Smiley
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright 2000-2004 Yet another Bulletin Board