# Can you solve the penniless pilgrim riddle? – Daniel Finkel

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, intersecting five more
that run north to south. You’re standing on the
northernmost street facing east, with the two blocks containing the gate
and the welcome center behind you. The temple’s only entrance lies
at the very southeast corner. It’s not a long walk,
but there’s a problem. As you learn from the brochure, Duonia imposes a unique tax
on all visitors, which must be paid when they arrive
at their destination within the city. The tax begins at zero, increases by two silver
for every block you walk east, and doubles for every block
you walk south. However, a recent reform
to make the tax fairer halves your total bill for
every block you walk north and subtracts two silver
for every block you walk west. Just passing through the gate
and the welcome center means you already owe four silver. As a pilgrim you carry no money
and have no way of earning any. What’s more, the rules
of your pilgrimage forbid you from walking over any stretch of
ground more than once during your journey— though you can cross your own path. Can you figure out a way to reach
the temple without owing any tax or walking the same block twice
in any direction? Pause here if you want
to figure it out for yourself. Answer in: 3 Answer in: 2 Answer in: 1 You look at the map
to consider your options. Walking towards the temple
always increases the tax, and walking away decreases it, so it seems like you can never reach it
without owing silver. But what happens when you walk
around a single block? If you start out owing four silver
and go clockwise starting east, your tax bill becomes six, then 12, then 10, then five. If you looped again, you’d owe seven, 14, 12, and six. It seems that each clockwise loop leaves
you owing one extra silver. What about a counterclockwise loop then? Starting owing four again
and going south first, your bill changes to eight, 10, five, and three. Looping again you’d owe six, eight, four, and two. Each counterclockwise loop actually earns
you one silver. That’s because any tax doubled, plus two, halved, and minus two, always ends up one smaller
than it started. The key here is that while the different
taxes for opposite directions may seem to balance each other out, the order in which they’re applied
makes a huge difference. You start off owing four silver, so four counterclockwise loops would
get you down to zero. Unfortunately, it’s not that simple,
since you can’t walk the same block twice. But there’s another way
to reduce your bill: walking one large counterclockwise loop
through the city. From your starting position,
walk three blocks south. You need to leave the southernmost
street clear for the final stretch, so continuing counterclockwise
means going east. Walk two blocks to the eastern wall
and you owe a whopping 36 silver. But now you can start reducing your bill. Three blocks north and one block west
cuts it to 2.5. You can’t go west from here
—that would leave you with no way out. So you go one block south,
and the remaining three blocks west, leaving you with a debt
of -1 silver. And since doubling a negative number
still gives you a negative number, walking the three blocks to the south wall
means the city owes you eight. Fortunately, that’s exactly enough to get you through the final blocks
to the temple. As you enter, you realize what
you’ve learned from your pilgrimage: sometimes an indirect route
is the best way to reach your destination.

## 100 thoughts on “Can you solve the penniless pilgrim riddle? – Daniel Finkel”

1. TED-Ed says:

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2. Kim Chen says:

The pilgrim can earn extra money! What a XXXX tax reformer!

3. Devin Hinkson says:

1st world problems….

Why can’t u just lie to the tax collector and say oh no I climbed over the wall, didn’t travel any blocks so not taxes 4 me 🤷‍♀️

5. TheMegax Plus says:

This is… tax evasion

6. Quang Nguyen says:

Pilgrims, some how existing when modern buildings are here. And how can a city be above the clouds?

7. rupesh acharya says:

She wasn't even walking !!

8. Xynnful says:

How you gonna get out now?

9. Huy Tran Dang says:

Ill just turn into satan and sweep that place

10. M Light says:

Well if you cannot walk the same block twice, then crawl

11. patrick zhang says:

I have another way and ended up with 21

12. Omar Naja says:

Um if you go straight east then straight straight south you will end up with 128 silver but while going back straight west then straight north you will end up with 0 again

13. thousand sunny says:

this is very interesting,
i would moonwalk facing west while going to 2 block east, making my tax 0
then just walk 4 block south like a normal pilgrim does

14. Burble Geggy says:

15. D H says:

She gets around for a nun.

16. Alejandro Rodriguez says:

Plot twist how do they get home

17. Rocky balboa says:

18. Pramila Verma says:

hey i have another solution for this question!

19. Yellow Diamond says:

Simple walk off of the kingdom and walk around it until you get to the temple.

20. shnuts says:

Just walk backwards

21. Gut Eater says:

So thats why religion doesnt get taxed

22. J Ahn says:

Welcome to Duonia you must pay your tax
Walks around NO U

23. User Name says:

But wait there's more, you are an old pilgrim, so old, that you cant walk more than 2 blocks without having to stop for the day. You have 3 days. Thankfully, though, there is a bus, but it costs 100 silver, bit will take you to your destination.

Answer: Use the power of God to move the temple closer to you or die trying

24. Bhargav Shiroya says:

Ok collect all money and throw all when you reach temple 😂😂😂😂😂😂

25. Luci Fate says:

Yasou quote right here

26. Catherine Chen says:

My dad found an alternative solution to the riddle, but you end up earning 2 silver.
Solution: starting from the welcome center, SWWSSEEEENNNWSWSWSSEEE.

27. THEMEMER GAMER says:

Just be a kid bc kids can't pay taxes

28. Shiiny Stqr says:

29. LightWarrior 3 says:

The name is cut off at "Can you solve the pennile…"

30. Jules Bianchi says:

#RIPANTHONIEHUBERT

31. Ruthie루띠 says:

RIDDLE

32. catfan1290 says:

How to win weeeeeeeee

33. Priyaa __ says:

You just go through the buildings…

34. Kx:zY says:

I solved it and had -28 silver in the end

35. THAT’S NOT HOW YOU SPELL MY NAAAME!!! BRO says:

Why not just crawl if you don’t want to pay the walking tax?

36. Htes Seth says:

It never said that it couldn't go South East.

37. Kelakotana says:

Buddhists & Muslims: TRIGGERED

38. cleveravi says:

Took 30 minutes but I f***ing solved it.
Edit: Looking at the solution it said the stuff that I stumbled on while trying to solve this.

39. aminoacidcereal says:

I would just pay on behalf of my stupidity

40. Zaahid Muhammed says:

It took me hours … HOURS!!!… trying to solve this riddle… did I? …

NO!

41. alfred veseli says:

i knew how to beat the riddle, but i just couldnt find the right pathway…

42. tommy lonergan says:

Did anyone else notice the Swastika ??

43. Srinithi Ramaiah says:

Ted Ed

44. Bruce Wayne says:

Solution:
Parkour!

45. Rodrigo Santino Pascual says:

46. Jason Sammons says:

The Ted-Ed(Daniel Finkel) solution is wrong because it is not the best path for the Pilgrim. The Pilgrim can earn 4 silver coins from a city that is exploiting people who are simply exercising and not sitting at their computer solving math riddles. The best path is DDLDRRRUUULDLLLDDDRRRR.

47. Jillian Patton says:

frick the temple i’m earning 100 bucks for randomly walking today 😂🤪

48. CHRISTOPHER DUTCHAK says:

Did this in school today. To over an hour and I still haven’t solved

49. nivriti vikram says:

I would give up my pilgrimage and switch religions.

50. Karim Amr says:

Good Job you did it!! Now sweetheart you gotta get out, and remember you cant walk on the same path twice (;

51. Chris says:

WHAT HAPPENS WHEN THEY DIVIDE THIER TAX WHILE AT ZERO?

52. A Nice Place To Live says:

How brain dead would the pilgrim be?

53. BudderMeow says:

What if you get negative tax, but say you already reached your destination so the government has to pay you? And then use that money to pay for your real destination?

54. Mr Gunka Official says:

I thought it said penisless

55. Kim McDonough says:

How did she get halfway down the first street without having to pay

56. ElitePlays says:

4:05 but it doesn't work like that

57. Michael Donodeo says:

Sweatcoin, get paid to walk

58. Nathan Robert Taylor says:

Moral of the story: Get a job and pay your tax

59. Samdaboss Gaming says:

Just walk out of city limits

60. Gacha_Clumsy says:

So in short : get closer and you get owed
get away and you owe them

Only ppl with IQ under 5 disliked this vid

62. Oska Ivanovich Smirnov says:

Imagine you lived in that town and you got diarrhea. That would be the worst place to live.

63. MartinSp3 says:

This is not the optimal solution. you can even end up with -4, i.e. the city owing you money!
You just have to make another small detour: in the beginning, don't walk south-south-south but south-south-east-south-west.

64. Ir0n Gamer says:

I wish I could get paid for running in a circle

Boi it's 2 in the morning why am I here

66. Squid 2 says:

How do you get out of the city?

67. Depressed Mid Life Crisis Timmy says:

It’s simple.

I just run to the temple, not walk there, lol. Oh, and just walk around counter clockwise 10 times and then run.

68. TT yler says:

Probably not

69. Avril Animates says:

The voice is strangely asmr

70. Mr Oof says:

I wonder how joggers feel

71. Ryun How Goh says:

I thought that it couldn't be below 0 at any period, so I deduced that it was impossible… bcoz any time you move closer the tax increases unless you move Southwards with 0 silvers owed… took 3 hours still didn't realise could have negative values…

72. Hermione Granger says:

Well i say screw those rules im applying to be a citizen there

73. Mahbob Ahmed says:

How To Cheat The System

74. Warp says:

TED-Ed: Can you solve the-
Me: No.

75. David Basa says:

Why she have to be a pilgrim why not just a person

76. Aaron Parker says:

How to get free money

Go here
Walk in cirlces

77. Camille la Lupo says:

stonks

78. Sila Brandon says:

How she gonna get back

79. MOOZIE B says:

Me: Yes! Finally made it to the temple!

How do I get back?

Welp, I guess this is my home now.

80. EpicFortnite7 says:

Imagine if some person walked in a loop and got stuck. It could happen, because they can’t walk the same ground twice, they would just be stuck. Unless… what if they crawled?

81. Khalid Majjouti says:

2x(-1)=-2 …?

82. StonkR says:

If you have tax that is on a negative number, would the government give you money or not?

83. Cunard Line: Spare Every Expense says:

And then you’re arrested for tax evasion.

84. Harry Murphy says:

okay we all say the same thing when we first looked at the title… don’t lie

85. Maxim L says:

0x2=2

86. dámgo, jáke says:

And that's how PEMDAS works.

87. Andy Chen-Yu Low says:

After leaving temple
Pilgrim: is rich

88. Uday Gawande says:

Always Fascinating ….
Great job
Salute TED-Ed……………… 🙂

89. that one guy c says:

Couldn't you also go down 1, left 2, down 2, Right 4, up 3, left 1, down 1, left 1, down 1, left 1, down 2, Right 3

90. Meglotron says:

I would have just taken the 8 silver lol

91. chubby - chan says:

you fly—

92. Panda Bear667 says:

Can we get more riddles TedEd? Your riddles light up my mind and make my day! Cheers from a 15 year old fan from Minnesota!

93. Masif says:

My friend: So what is your job? Mine is a Doctor
Me: uhhh it's complicated

94. The rise of the Freg says:

"Not all who wonder are lost"
But I sure am

95. Redheart Girly says:

Just drive

96. BroCraft says:

Day 3

Walked around my house like 300 times now. Hope I become rich

97. P4RA90N YT says:

Just go around 1 counter clock wise infinate times😏

98. xuan pang says:

Most people: walks counterclockwise
Bill gates: walks clockwise

99. Rosemary Stanley says:

Entering from the pacifica northwest