Safe Generals

You have 7 generals and a safe with many locks. You assign the generals keys in such a way that EVERY set of four generals has enough keys between them to open ALL the locks; however, NO set of three generals is
able to open ALL the locks. How many locks do you need, and list how many keys does the first general get, the second, … Is there more than one way that works?

Communicated by Travis ([email protected])

Posted in Combinatorics, Hard

13 Comments

  1. Steven Miller on August 24, 2012 at 3:42 pm

    Lukas: email me at sjm1 AT williams.edu == looks good //s



  2. Steven Miller on August 24, 2012 at 3:41 pm

    Lukas: correct — please email me directly at sjm1 AT williams.edu to discuss the other riddles (I prefer not to post the solns)



  3. Steven Miller on August 11, 2012 at 2:20 am

    John: correct; email me at sjm1 AT williams.edu to discuss



  4. Anonymous on July 24, 2012 at 4:01 pm

    Got 35 locks but but i defintily did it the long way, Each general gets 20 keys

    It helps to make the problem smaller at first.



  5. Steven Miller on February 4, 2012 at 7:32 pm

    I’ll send a hint first….



  6. Brett on February 4, 2012 at 5:13 pm

    I would like to know the answer with an explanation please.



  7. Steven Miller on January 26, 2012 at 6:47 pm

    Great start!But you need more than 13 locks….



  8. Beau on January 26, 2012 at 6:36 pm

    It looks like you’d need at the very least 13 locks. Some generals get 7 keys, some get 8.
    G1=L1, L5, L6, L7, L8, L12, L13
    G2=L1, L2, L6, L7, L8, L9, L13
    G3=L1, L2, L3, L7, L8, L9, L10
    G4=L1, L2, L3, L4, L8, L9, L10, L11
    G5=L2, L3, L4, L5, L9, L10, L11, L12
    G6=L3, L4, L5, L6, L10, L11, L12, L13
    G7=L4, L5, L6, L7, L11, L12, L13



  9. Steven Miller on January 9, 2012 at 4:58 am

    Ali; correct, well done — not posting as it’s the answer. //s



  10. Steven Miller on December 12, 2011 at 2:25 am

    You get to decide how many locks to have. Say you choose to have L locks. For each lock, you can get 1,2, 3, 4, 5, 6 or 7 keys made. You then choose which generals get keys to which locks. You could give everyone a key to each lock, but then you could open it with just one person! You need to assign keys in such a way that no matter which three generals get together, they are unable to open ALL of the locks (so at least one of the L locks does not have a key among the 3 generals chosen; depending which 3 generals we look at, it will be a different lock); however, EVERY set of four generals will have at least one of the assigned keys for each of the L locks.



  11. Kareem on December 11, 2011 at 9:33 pm

    soo 4 keys for 4 locks? one key per general per lock? thats why 3 generals can’t open it? i’m not sure what exactly i’m supposed to do here..



  12. Steven Miller on October 5, 2011 at 1:58 am

    each lock has its own key, and it only takes one key to open a given lock.



  13. [email protected] on October 4, 2011 at 6:59 am

    I’m pretty sure that I understand this irrcorrectly.

    Cause in way that i get it, u just give 1 key to each of general and put 4 locks to safe.
    So u need least 4 general to open safe and 3 cant do it.

    But there is something what I miss, am I right ?



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