Sun Gate to Moon Gate
Read the puzzle
A map links Sun to Moon through four towers and three oases. Roads, in days: Sun-Tower 1, 4; Sun-Oasis 2, 3; Tower 1-Oasis 1, 3; Tower 1-Tower 2, 3; Oasis 1-Tower 3, 4; Oasis 2-Tower 2, 4; Oasis 2-Oasis 3, 5; Tower 2-Tower 3, 3; Tower 2-Tower 4, 5; Oasis 3-Tower 4, 2; Tower 3-Moon, 4; Tower 4-Moon, 3. Fewest days from Sun to Moon?
Fewest days from sun to moon?
13 DAYS
Two oases then a tower: 3 + 5 + 2 + 3 = 13.
How to solve it
Work outward from the Sun and write the fewest days needed to reach each stop, always keeping the smaller total.
From the Sun: Oasis 2 takes 3 days and Tower 1 takes 4. From there: Tower 2 can be reached as 4 + 3 = 7 or 3 + 4 = 7, so 7. Oasis 1 is 4 + 3 = 7. Oasis 3 is 3 + 5 = 8.
Next layer: Tower 3 is 7 + 3 = 10 through Tower 2, or 7 + 4 = 11 through Oasis 1, so 10. Tower 4 is 8 + 2 = 10 through Oasis 3, or 7 + 5 = 12 through Tower 2, so 10.
Last step: the Moon is 10 + 4 = 14 from Tower 3, or 10 + 3 = 13 from Tower 4. The best route is Sun, Oasis 2, Oasis 3, Tower 4, Moon: 3 + 5 + 2 + 3 = 13 days.
The usual wrong answer is 14, from the route that looks direct across the middle, Sun, Tower 1, Tower 2, Tower 3, Moon, which is 4 + 3 + 3 + 4. It avoids the 5-day road, but the short 2-day and 3-day roads at the bottom more than make up for it.
Learn the method: Shortest Route Puzzles: How to Find the Fewest Steps by Hand
