A BIT CONFUSING...........

Number Theory Level 2

There are 4 friends who want to cross a bridge. Only 2 people can walk on the bridge at a time. The times taken by the 4 friends to cross the bridge individually are 1min., 2 mins., 5 mins. and 10 mins. respectively. They have got just one torch with them and there is complete darkness around. What is the minimum possible time that they all will take to cross the bridge?

DETAILS AND ASSUMPTIONS: 1) No one can walk in darkness. All of them need the torch. 2) When two friends walk together, the friend who takes the most time is considered to be the equivalent time. For eg- When the friend who takes 1 min. and the one who takes 10mins. walk together, the equivalent time taken would be 10 mins.


The answer is 17.

Shreyas Garkhedkar by shreyas garkhedkar , 21, India

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1 solution

  • Let's set friend A takes 1 min. to cross the bridge, B takes 2 minutes, C takes 5 minutes and D takes 10 minutes.
  • First crossing: A and B , (2 min).
  • Second crossing: A comes back (2 + 1 = 3 min).
  • Third crossing: C and D , (3 + 10 = 13 min).
  • Fourth crossing: B comes back (13 + 2 = 15 min).
  • Fifth and last crossing: A and B again, combining for (15 + 2) = 17 minutes!!
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