Riddles, brain puzzles and mathematical problems

**BAndrew** · 03-25-2014, 01:51 AM

Neptune is on fire!

You got it again Smile

There are actually many ways you can do it, but you got the key idea that you can use 2^10 = 1024>1000 possible combination of rats. Therefore 10 rats is the minimum requirement. All you have to do is to associate the combinations with certain bottles.

Well done.

EDIT:I am going to take a rest. I'll probably post another problem tommorow.

**MyRedNeptune** · 03-25-2014, 01:55 AM

(03-25-2014, 01:51 AM)Titanomegistoterastiotatos Wrote: Neptune is on fire!

You got it again

There are actually many ways you can do it, but you got the key idea that you can use 2^10 = 1024>1000 possible combination of rats. Therefore 10 rats is the minimum requirement. All you have to do is to associate the combinations with certain bottles.

Well done.

Yay! Actually, I'm stupid. I just realized that I don't even need to use 2 rats for each step. Instead, I can use just 1, making the minimum number of rats 9 instead of 18.

I'll go edit my post to reflect that.

**BAndrew** · 03-25-2014, 02:04 AM

Yeah but that's a detail, I am mainly interested in the thought process which is correct so I didn't mind about it.

Wait 9 rats? I count 10.

1024 = 2^10 = 10 steps right?

**MyRedNeptune** · 03-25-2014, 02:10 AM

(03-25-2014, 02:04 AM)Titanomegistoterastiotatos Wrote: Yeah but that's a detail, I am mainly interested in the thought process which is correct so I didn't mind about it.

Wait 9 rats? I count 10.

Yeah, since there is no need to check whether there is any poison in 1000 bottles, we start from 512 = 2^9.

**BAndrew** · 03-25-2014, 02:34 AM

Rat 1:512
Rat 2:256
Rat 3:128
Rat 4:64
Rat 5:32
Rat 6:16
Rat 7:8
Rat 8:4
Rat 9:2
Rat 10:1

Think if it were 2 bottles for instance:

In that case you need 1 (because 2^1) rat to determine which bottle has the poison and not 0 (2^0)

Generalizing the problem you can find a poisonous bottle among 2^n bottles with just n rats.

NOTE: Because in this problem there are 1000 bottles and not 1024 you might need less than 10 rats on very specific cases. However, the minimum safe ammount of rats (in order to be 100% percent sure) is 10.

**MyRedNeptune** · 03-25-2014, 02:45 AM

(03-25-2014, 02:34 AM)Titanomegistoterastiotatos Wrote: Rat 1:512
Rat 2:256
Rat 3:128
Rat 4:64
Rat 5:32
Rat 6:16
Rat 7:8
Rat 8:4
Rat 9:2
Rat 10:1

It's probably better I look at this tomorrow because I am really tired

Ah whoops, you're right. I had the same list written out on my paper, but apparently I missed the 8. Blush

How embarrassing.

Well, I suppose we're even now. Tongue

Thanks for the correction.

EDIT: It's all correct now.

**BAndrew** · 03-25-2014, 02:49 AM

Alright then.

PS. It's almost there is a curse that when you solve a problem in all your excitement you are going (for certain) to make a silly miscalculation and ruin it.

Tomorrow I'll post another problem (unless someone wants to share another).

**MyRedNeptune** · 03-25-2014, 03:04 AM

(03-25-2014, 02:49 AM)Titanomegistoterastiotatos Wrote: PS. It's almost there is a curse that when you solve a problem in all your excitement you are going (for certain) to make a silly miscalculation and ruin it.

Gosh, I know right?

**Bridge** · 03-25-2014, 12:42 PM

I don't get it. The last rat still receives "512" bottles so it is impossible to find the poison in only 24 hours, wasn't that the point of the puzzle? You said it takes 10-20 hours for the poison to run its course and the scientist only has 24 hours to find the poison, implying that in a worst case scenario it must be done in one go (though it is possible to do it in two in if the poison decides to kill quickly.) Therefore, to satisfy the conditions of the puzzle it must be done in one go. With this method, ruling out 512 bottles is only the first step, you must then divide 512 bottles the same way, and then 256, then 128, etc … until you have only two. Therefore, way more than 24 hours and way more than 10 rats are required.

**BAndrew** · 03-25-2014, 01:56 PM

(03-25-2014, 12:42 PM)Bridge Wrote: I don't get it. The last rat still receives "512" bottles so it is impossible to find the poison in only 24 hours, wasn't that the point of the puzzle? You said it takes 10-20 hours for the poison to run its course and the scientist only has 24 hours to find the poison, implying that in a worst case scenario it must be done in one go (though it is possible to do it in two in if the poison decides to kill quickly.) Therefore, to satisfy the conditions of the puzzle it must be done in one go. With this method, ruling out 512 bottles is only the first step, you must then divide 512 bottles the same way, and then 256, then 128, etc … until you have only two. Therefore, way more than 24 hours and way more than 10 rats are required.

Time limit. Ooops. I completely forgot. You are right. The method Neptune used can be done with 10 rats but it will take much more than 24 hours because you must wait 10-20 hours for the first rat to die. Sorry for that. It was late when I checked his solution and it slipped my mind.

Hint:The answer is 10 rats (as Neptune predicted), but you have to modify Neptune's method to make it faster

EDIT: Actually it is correct (see following posts)