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Posers and Puzzles

Posers and Puzzles

  1. Standard member PBE6
    Bananarama
    07 Jun '05 19:05
    OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?
  2. Standard member PBE6
    Bananarama
    07 Jun '05 21:20
    Originally posted by PBE6
    OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?
    Hmm. Actually, this is a stupid puzzle. There's no defined answer. Consider this one instead: the ant digs up chunks 0.01 metres deep. Now how long does it take to burrow through?
  3. Donation richjohnson
    TANSTAAFL
    07 Jun '05 21:23
    312.5s
  4. 07 Jun '05 22:44
    Originally posted by PBE6
    OK, here's a relatively simple puzzle. Say there's an ant trying to burrow through a slab of dirt 1 metre thick. The ant crawls at 0.2 metres per second, and digs at a rate of (1/60) m/s. The ant must also carry all the dirt it removes out to the entrance to make room for more tunneling. How fast can it dig through the slab?
    The quickest way is for it to burrow all the way through and then carry all the dirt out.

    This would take 60 secs + 5 secs = 65 secs
  5. 07 Jun '05 22:51
    Originally posted by PBE6
    Hmm. Actually, this is a stupid puzzle. There's no defined answer. Consider this one instead: the ant digs up chunks 0.01 metres deep. Now how long does it take to burrow through?
    It has to dig up one metre, that takes 60s
    the time it has to spend walking is the sum from n=1..100 of n/10 which is 50.5*100/10, i.e 505s

    so I make it that the ant takes a total of 565s
  6. Donation richjohnson
    TANSTAAFL
    07 Jun '05 23:13 / 1 edit
    Originally posted by iamatiger
    It has to dig up one metre, that takes 60s
    the time it has to spend walking is the sum from n=1..100 of n/10 which is 50.5*100/10, i.e 505s

    so I make it that the ant takes a total of 565s
    Walking time = 50.5m * 5s/m = 252.5s

    edit:
    oops - I forgot that the ant has to walk back down after removing the dirt, making it 101m of total walking distance, and 565s total time, as you already stated.