Friday puzzle -- wine tasting

Re: Friday puzzle -- wine tasting

1000 bottles of wine on the wall

1000 bottles of wine

Take one down

Pass it around

999 bottles of wine on the wall

...

Give me 10 slaves and another two cases of wine and I'll figure it out.

;-)

But you don't need the other two cases of wine, and are you minimizing the number who will die (given the minimum number of testers?)

Looks like I need to find some harder material for you! :-)

Re: ;-)

The other two cases are not a requirement, but you could handle up to that many bottles with 10 testers.

With 1000 bottles, you would probably end up with less than 5 dead testers. The worst case scenario would be 9.

Save another prisoner

You can actually lower the worst case to 8 dead bodies (and still test a little more than one additional case). When numbering the bottles, skip 511, 767, 895, ...

Now, this discussion should give enough hints for some others to chime in?

Blending and binary was my first thought

Seems like I have the right idea based upon the banter...:-)

Re: Blending and binary was my first thought

Yes, I'd say so!

Nice optimization

I hadn't thought of that.

Of course, if you start numbering at zero, you have a 0.1% chance that nobody dies.

None!

How many guests are expected and how big are the bottles. If he sets up his party right, no slaves need to die. Worst case he loses 4-6 guests if he makes the seating 4-6 to a table. One bottle of wine per table, that's about 6,000 guests so losing 6 is less than .1% of the guests, leaving him with 100% of his slaves. Since death isn't immediate, he can always blame it on the potato salad being bad. ;)

Lee

Re: Save another prisoner

I don't have it, but shouldn't the value of wine vs slave be factored in too? As in it might be better to narrow it down to ~.8 percent of the bottles.

another approach

Opening and blending wne loses to much product, time and slaves.

Give the 1000 bottles to the king next door (that you don't much like anyway) and buy new wine. No lost slaves or guests and in a testing process

wine tasting solution

Bill, Steve, and possibly Ed nailed the basic approach.

Lee and Gary get points for outside the box solutions.

Number the bottles from 0 to 1004, skipping 511, 767, 895, 959, and 991. Express each of those numbers in binary form, each of which will have ten places, with 2 to 10 zeros and 8 to 0 ones. (The numbers we skipped had 9 ones).

Now get ten vials, numbered 0-9. From each bottle, take an eyedropper of wine, and put a drop in each vial whose number corresponds to the place of a 1 in the wine's number. Get a different slave to drink from each vial. The ones that die indicate the 1's in the binary representation of the poisoned bottle.