During his 27-day trek, the outback Explorer had plenty of time to reflect on the difficulties he had experienced in ensuring sufficient supplies for his entire trip. A few calculations made him realize that had he used the local natives to carry some of his supplies, he could have completed the 280 km cross desert trek in just seven days: a savings of nearly 3 weeks! What is the minimum number of bearers the Explorer would need to employ in order to make the crossing in just seven days, given that, only 40 km can be travelled in any one day and only four days' supplies can be carried by any one man, and given also that Explorer and bearer alike need a full day's ration every day? [assume, in this puzzle that extreme climatic conditions would make it impossible for supplies to be safely cashed along the way.] Good luck and have fun. Happy New Year to all.
I believe there are several solution for this type of puzzle due to the number of combinations possible.
Here is one solution that requires 4 men and the Explorer.
Let the natives be represented by letters A, B, C, and D and the Explorer by E. The crossing might occur like this:
Day 1: A, B, C and E set out on the first 40 km.
Day 2: A gives both B and E one day's rations and returns to base. B, C and E set out on the next 40 km.
Day 3: C gives E a day's rations and returns to the first camp [set up at the end of Day 1]. B and E set out on the next 40 km. In addition, A, who has returned to base, sets off with three days rations to the first base 40 km away. D also sets off for first base, but with 4 days rations.
Day 4: A has met up with C and gives him a day's rations. Both men return to base. B gives E a day's rations and sets off back to the second camp [80 km from base]. E now has sufficient supplies to complete the crossing unassisted. D sets off from the first camp bound for the second.
Day 5: E continues on his way. D, who has met up with B, shares his rations with B and both make their way to the first camp. A, with four days rations, also makes his way to the first camp.
Day 6: E has only two days to go. A has met up with B and D and the three return to base camp, sharing the rations A has left.
Day 7: E completes his crossing.
