Can you solve the penniless pilgrim riddle? - Daniel Finkel

TL;DR

Find a way to reach the temple in Duonia without owing any tax or walking the same block twice.

Transcript

After months of travel, you’ve arrived at Duonia, home to the famous temple that’s the destination of your pilgrimage. Entering from the northwest, you pass through the city gates and the welcome center, where you’re given a map and a brochure. The map reveals that the town consists of 16 blocks, formed by five streets that run west to east, in... Read More

Key Insights

• 🚕 Duonia has a unique tax system that increases tax when walking east, doubles tax when walking south, halves tax when walking north, and decreases tax when walking west.
• 🚕 Walking counterclockwise reduces the tax bill by strategically utilizing the tax system's rules.
• 🥈 Each counterclockwise loop in Duonia earns one silver.

Questions & Answers

Q: What is the unique tax system in Duonia?

Duonia imposes a tax on visitors that increases by two silver for every block walked east, doubles for every block walked south, halves for every block walked north, and decreases by two silver for every block walked west.

Q: What are the rules for the pilgrimage in Duonia?

Visitors on a pilgrimage in Duonia are not allowed to walk over any stretch of ground more than once but can cross their own path.

Q: Can you reach the temple without owing any tax?

Yes, it is possible to reach the temple without owing any tax by strategically walking a counterclockwise loop through the city, utilizing the unique tax system's rules to reduce the tax bill.

Q: How does walking counterclockwise reduce the tax bill in Duonia?

Walking counterclockwise reduces the tax bill because the tax system applies different taxes to opposite directions in a specific order, ultimately resulting in a smaller tax bill. Each counterclockwise loop earns you one silver.

Summary

In the city of Duonia, pilgrims must pay a unique tax when they reach their destination. The tax increases by two silver for each block walked east and doubles for each block walked south. However, a recent reform decreases the tax for each block walked north and subtracts two silver for each block walked west. Pilgrims cannot walk the same block twice, but can cross their own path. The challenge is to reach the temple without owing any tax or retracing steps.

Questions & Answers

Q: How is the tax calculated in Duonia?

In Duonia, the tax increases by two silver for each block walked east and doubles for each block walked south. If a pilgrim walks north, the tax is halved, and if they walk west, two silver is subtracted from the tax.

Q: What happens when a pilgrim walks in a clockwise loop around a block?

Walking in a clockwise loop starting from owing four silver, the tax bill becomes six, then 12, then 10, then five. Looping again, the pilgrim would owe seven, 14, 12, and six silver. It seems that each clockwise loop results in owing one extra silver.

Q: Is there a way to reduce the tax owed through counterclockwise loops?

Yes, counterclockwise loops can actually earn the pilgrim one silver. Starting from owing four silver, a counterclockwise loop going south first changes the bill to eight, 10, five, and three. Looping again, the pilgrim would owe six, eight, four, and two silver. Each counterclockwise loop earns one silver because the tax calculations result in a value one silver smaller than the previous calculation.

Q: Can a pilgrim reach the temple without owing any tax or retracing steps?

Yes, there is a way to reach the temple without owing any tax or retracing steps. The pilgrim can walk one large counterclockwise loop through the city. They start by walking three blocks south from the starting position, then go two blocks east to the eastern wall, which results in owing 36 silver. However, by walking three blocks north and one block west, the tax is reduced to 2.5 silver. They cannot go west from this point, so they go one block south and then three blocks west, resulting in a debt of -1 silver. Doubling a negative number still gives a negative number, so the pilgrim walks three blocks south to the south wall, and the city owes them eight silver. With this, the pilgrim can complete the final blocks to reach the temple.

Takeaways

The journey in Duonia teaches the pilgrim the lesson that sometimes taking an indirect route is the best way to reach a destination. By strategically navigating around the city and understanding the tax calculations, the pilgrim is able to reach the temple without owing any tax or retracing steps.

Summary & Key Takeaways

• Duonia is a city with a unique tax system where the tax increases as you walk east, doubles as you walk south, halves as you walk north, and decreases as you walk west.

• The challenge is to reach the temple without owing any tax or walking the same block twice.

• By walking a counterclockwise loop through the city, strategically reducing and utilizing the tax system, it is possible to reach the temple without owing any tax.