Unutterably Silly Quiz

[Bilbo1967]

Originally Posted by pdurrant

OK, a quick logical/mathematical one. (Thanks, Dara O Briain!)

A bank is implementing security on their main vault. There are four people authorised to hold keys for the vault, and the bank wants any three of the four keyholders to be able to open the vault together, but any two people must not be able to open the vault on their own.

What is the minimum number of separate locks the vault must have, and how must keys be assigned to the four key holders?

From the School of Hard Sums (or similar)? I've been watching that series, but must have missed that episode. Hang on while I check i-Player

[Daithi]

I've figured out how to do it using just 5 locks--

Employee 1 has K1, K2, K5
Employee 2 has K2, K1, K4
Employee 3 has K3, K2
Employee 4 has K4, K3

Edit: Employee 1 & 4 could open the vault, so never mind.

[pdurrant]

Originally Posted by Daithi

I'm not positive this is the minimum number locks and keys, but it does work--

Six locks with each employee receiving three keys.

Employee 1 has K1, K2, K3
Employee 2 has K4, K1, K6
Employee 3 has K5, K2, K4
Employee 4 has K6, K3, K5

No two employees have more than two keys that go to the same lock, so three employees are required to open all the locks. Plus no two employees hold all different keys.

Exactly right. Well done!

One easy way to look at is is this: for every pair of employees, there must be one lock on the vault for which they do not both have keys. With four employees, there are six pairs. So there must be six locks.

[pdurrant]

Originally Posted by Bilbo1967

From the School of Hard Sums (or similar)? I've been watching that series, but must have missed that episode. Hang on while I check i-Player

Yes, that's the series. Splendid stuff.

[Daithi]

Sorry for the delay, but it took me a little while to write up this quiz. This is a "find the links" quiz, but with a twist. One of the items in each list doesn't belong. So what is the links of items 1-10, and what is their overall link?

1. Flamingo, Texas, Chuck Norris, Pink Power
2. Fellowship of Catholic University Students, Binoculars, Microscope, Royal Society
3. Neil Armstrong, Jacques-Yves Cousteau, Leif Ericson, The Incredible Hulk
4. Scotland, Driver, Eagle, Piano
5. Belle de Jour, Hillary Clinton, Heidi Fleiss, Eliot Spitzer
6. Czar, Dung, Lennon, Deathwatch
7. Oslo, Camp David, Helsinki, Juno
8. Snoop Dogg to Dr. Dre, Eminem to Dr. Dre, 50 Cent. to Dr. Dre, Biggie Smalls to Dr. Dre
9. Emergency, Cheeses, Towers, September
10. Elk, Cheetah Food, Antelope, Gazelle

Figure out the overall link and they become a lot easier -- but if you reveal it too soon it makes easier for your competitors as well.

1.Chuck Norris
2. Fellowship of Catholic University Students,
3. The Incredible Hulk
4.
5. Hillary Clinton
6.
7. Juno
8. Biggie Smalls to Dr. Dre
9 Cheeses
10. Elk

[PeterT]

4 Golf - Piano is the odd one

[Daithi]

PeterT has number 4.

Hamlet is on the wrong track. You have to give the link, not the thing that doesn't belong.

[Bookpossum]

6. Beetles.

[Bookpossum]

5. Prostitutes.

[Bookpossum]

7. Accords

[Bookpossum]

10. African savannah?

[Daithi]

1. Flamingo, Texas, Chuck Norris, Pink Power
2. Fellowship of Catholic University Students, Binoculars, Microscope, Royal Society
3. Neil Armstrong, Jacques-Yves Cousteau, Leif Ericson, The Incredible Hulk
4. Scotland, Driver, Eagle, Piano -- Golf -- PeterT
5. Belle de Jour, Hillary Clinton, Heidi Fleiss, Eliot Spitzer
6. Czar, Dung, Lennon, Deathwatch -- Beatle -- Bookpossum
7. Oslo, Camp David, Helsinki, Juno -- Accord -- Bookpossum
8. Snoop Dogg to Dr. Dre, Eminem to Dr. Dre, 50 Cent. to Dr. Dre, Biggie Smalls to Dr. Dre
9. Emergency, Cheeses, Towers, September
10. Elk, Cheetah Food, Antelope, Gazelle

[Bookpossum]

10. Herbivores.

[PeterT]

5 - Prostitutes; Hillary Clinton