River Crossing

Four people \(A,B,C,D\) need to cross a bridge carrying one torch. At most two cross at once, and any pair walks at the slower’s pace. Times: \(A=10\), \(B=5\), \(C=2\), \(D=1\). What is the minimum total time to get all across?

Answer

  1. Send \(C\) and \(D\) across: \(2\) min.

  2. \(D\) returns with torch: \(1\) min.

  3. Send \(A\) and \(B\) across: \(10\) min.

  4. \(C\) returns with torch: \(2\) min.

  5. Send \(C\) and \(D\) across again: \(2\) min.

Total time: \(2 + 1 + 10 + 2 + 2 = 17\) minutes.

Notes and comments

Comment 1: The key is to send the 10-minute and 5-minute persons together—sending them separately wastes too much time—and not to do that on the first crossing, since you’d then have to return with a slow person.

Back to collection