Logic Puzzles

Exploring Mount Neverest


Difficulty:

Professor Walkingholme, one of the exploring party, was allotted the special task of making a complete circuit of the base of the mountain at a certain level. The circuit was exactly a hundred miles in length and he had to do it all alone on foot. He could walk twenty miles a day, but he could only carry rations for two days at a time, the rations for each day being packed in sealed boxes for convenience in dumping. He walked his full twenty miles every day and consumed one day's ration as he walked. What is the shortest time in which he could complete the circuit?

ANSWER

Dump 5 rations at 90-mile point and return to base (5 days). Dump 1 at 85 and return to 90 (1 day). Dump 1 at 80 and return to 90 (1 day). Dump 1 at 80, return to 85, pick up 1 and dump at 80 (1 day). Dump 1 at 70 and return to 80 (1 day). Return to base (1 day). We have thus left 1 ration at 70 and 1 at 90. Dump 1 at 5 and return to base (1 day). If he must walk 20 miles he can do so by going to 10 and returning to base. Dump 4 at 10 and return to base (4 days). Dump 1 at 10 and return to 5; pick up 1 and dump at 10 (1 day). Dump 2 at 20 and return to 10 (2 days). Dump 1 at 25 and return to 20 (1 day). Dump 1 at 30, return to 25, pick up 1 and dump at 30 (1 day). March to 70 (2 days). March to base (l1/2 days). Total, 231/2 days.

A few claims have been made for fewer than 231/2 days, but they were all based on tricks that were actually, or in spirit, forbidden, such as dumping only portions of the sealed boxes, making the man take a long march fasting, or making him eat his day's ration before starting so as to carry and dump two rations. In the last case he would reaJIy be carrying three rations, one inside and two on his back!

If the route had been in a straight march across a desert, the shortest time necessary would be 86 days, as follows:

Dump 42 at 10, return to base (42 days). Dump 1 at 15, return to 10 (1 day). Dump 20 at 20 and return to 10 (20 days). Dump 1 at 20 and return to 15, pick up 1 and dump at 20 (1 day). Dump 10 at 30 and return to 20 (10 days). Dump 1 at 35, return to 30 (1 day). Dump 4 at 40 and return to 30 (4 days). Dump 1 at 40 and return to 35. Pick up 1 and dump at 40 (1 day). Dump 2 at 50 and return to 40 (2 days). Dump 1 at 55 and return to 50 (1 day). Dump 1 at 60 and return to 55. Pick up 1 and dump at 60 (1 day). March to base (2 days). Total, 86 days.

See also:
Baxter's Dog (Difficulty: 2)
"Simple" Arithmetic (Difficulty: 2)
The Thrifty Grocer (Difficulty: 3)
The Ambiguous Clock (Difficulty: 3)
Hill Climbing (Difficulty: 3)
The Cost Of A Suit (Difficulty: 2)
A Dreamland Clock (Difficulty: 3)
Dividing The Legacy (Difficulty: 2)

Logic Puzzles