Anyone able to help me solve a brain teaser i am stuck on?

Spurst

Golden Member
Aug 17, 2000
1,516
0
71
Finally, a puzzle that is mathematically quite intricate - a scheduling problem from Sangraal. This occurs in the endgame, when the Sangraal (Holy Grail) is almost won. You arrive at the castle where the Foul Fiend has imprisoned 8 knights. These are as follows:


Agravain - lightly bound - badly wounded;
Bors - lightly bound - scratched;
Caradoc - bound a bit more - badly wounded;
Dagonet - bound as C - scratched;
Ector - bound and gagged - somewhat wounded;
Feirefiz - in chains - badly wounded;
Gareth - in chains and gagged - somewhat wounded;
Harry - bound really tight in chains (poor chap) - scratched.

Here the state of binding means that it will take 1, 1, 2, 2, 3, 4, 5 and 6 minutes (respectively) to free them: a freed knight then goes away to wash and recover himself physically in time for the Sangraal's arrival. The time he takes for this second stage is 5, 10 or 15 minutes, according to injury. In twenty minutes' time the sun will set and the Sangraal will arrive. How many knights can you bring? We see, for example that if you want F, you must free him almost at once, as he can only be ready in 19 minutes at the earliest. Freeing Harry, though it takes 6 minutes, is not urgent, as he only needs to be freed by the 15th minute. This sort of puzzle has standard algorithms for solving it, but it is at least a bit more interesting than the average optimization exercise!
 

Spurst

Golden Member
Aug 17, 2000
1,516
0
71
i'm pretty sure the answer is 7...

there is a forumula for solving these things, i just dont know which it is.
 

b0mbrman

Lifer
Jun 1, 2001
29,470
1
81


<< i'm pretty sure the answer is 7...
there is a forumula for solving these things, i just dont know which it is.
>>


I'd start by rewriting the list with the numbers in the next two columns instead of the description...then go from there
 

b0mbrman

Lifer
Jun 1, 2001
29,470
1
81
Here, start with this...

Agravain - lightly bound - badly wounded; 1 15
Bors - lightly bound - scratched; 1 5
Caradoc - bound a bit more - badly wounded; 2 15
Dagonet - bound as C - scratched; 2 5
Ector - bound and gagged - somewhat wounded; 3 10
Feirefiz - in chains - badly wounded; 4 15
Gareth - in chains and gagged - somewhat wounded; 5 10
Harry - bound really tight in chains (poor chap) - scratched. 6 5
 

b0mbrman

Lifer
Jun 1, 2001
29,470
1
81
Summing horizontally...

Agravain - lightly bound - badly wounded; 1 15 16
Bors - lightly bound - scratched; 1 5 6
Caradoc - bound a bit more - badly wounded; 2 15 17
Dagonet - bound as C - scratched; 2 5 7
Ector - bound and gagged - somewhat wounded; 3 10 13
Feirefiz - in chains - badly wounded; 4 15 19
Gareth - in chains and gagged - somewhat wounded; 5 10 15
Harry - bound really tight in chains (poor chap) - scratched. 6 5 11
 

SOSTrooper

Platinum Member
Dec 27, 2001
2,552
0
76
I think you can free half of the knight, go to the next knight, and come back to free the rest of him... I guess?