I just read Dr. No by Percival Everett. It contains a maths riddle that I cannot get my head around. I tried searching online but I couldn’t find any answers.
Here’s the riddle:
There are three sheepherders who come to a bridge controlled by a troll and his two sons. He demands of them thirty sheep before they can pass. Each shepherd cuts out ten sheep from his flock and they give them to the troll. Once they have crossed, the troll decides that he should only have asked for twenty-five. He sends his sons after the men with five sheep. The sons decide to keep one sheep each and give three back to the herders. They do. Now it is the case that each shepherd has paid only nine sheep. Nine times three is twenty-seven. The trolls kept two. Twenty-seven plus two is twenty-nine. Where is the missing sheep?
Can anyone help me understand?
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30 sheep are given.
Troll has 30 sheep
Troll returns 5, kids keep two, return three
Shepherds have 3 back, kids have two, troll has 25
Shepherds gave 27 sheep (3*9) = 25 (troll) +2 (kids)
The trolls keeping two should subtract not add (in your write up)
Shepherders Troll Sons 30 30 25 5 3 25 2 Everything is fine, up until this bit:
Twenty-seven plus two is twenty-nine.
The total amount given to the troll and sons were 27 sheep (25 and the sons kept 2).
Where it gets confused is saying “The trolls kept 2” as if this were 2 more sheep on top of the 27 sheep. This leads to you erroneously getting to 29 sheep somehow. The 2 sheep are part of the 27, you can’t do this.
The 3 other sheep out of the original 30 are now with the shepherders after the sons came and returned them.
To add to this, “Where is the missing sheep?” is an example of a leading question. The question is based on the assumption that there is a missing sheep, when in fact there isn’t, leaving you flustered as you try and reconcile that.
This assumption is emphasised by framing the erroneous 29 you’ve created (where you’ve added this random extra 2 sheep) against the original 30.
If you paired up the actual number (27) against 30 instead, you would have the total number of sheep given back to the shepherders (3).
All sheep are accounted for here, as long as you do your maths correctly.
Ah, thanks! I knew I’d read something like this before, but all my searches were for trolls and sheep, so nothing came up!
There were 30 sheep involved in the original transaction.
The troll has 25.
His sons have 2.
The shepherds have the 3 that were returned.
To look at it the other way, the shepherd paid a net amount of 27 sheep. The troll has 25, his sons have the other 2.
You don’t add the 27 and the 2 - the 27 is the total of the 25 and the 2.
You don’t add the 27 and the 2 - the 27 is the total of the 25 and the 2.
Thanks - this is the explanation that I finally understood!
The problem here is that the riddle tricks you into thinking the total at the end should be 30, but because the herders originally give 30, but then get 3 back, the new total of sheep that changed hands is actually 27. In the end, the troll has 25 sheep and his sons have 2 sheep, 25 + 2 = 27 so all sheep are accounted for.
The first give 30, but the troll gives back 5, so they keep 25 sheep. The trolls kids keep 1 sheep each, so the sheaperds only get 3 back. 30 minus 3 is 27. 9 plus 9 is 18 plus 9 is 27. The riddle lied to you.
It didn’t lie. At the end it says 27+2=29, which is true. But it’s an irrelevant fact. The answer is: there are no missing sheep.
There isn’t one. 25 stay with Daddy Troll. The sons have 2 and each of the 3 herders get one back. That’s all 30.
In net, the transaction is for 27 sheep, with 25 being kept by the troll father and 2 by the troll sons, so 25+2=9+9+9.
I think I get that, but I still don’t understand who has the ‘missing sheep’ from the original 30. Is it the troll father or the shepherds?
EDIT: Hang on, I got it now. There’s no missing sheep, the riddle tricks you into adding the wrong numbers together!
Exactly. More precisely, the wording is making the reader confuse assets and debts. Which side of the ledger does that sheep actually belong on?
It’s more like they’re using the wrong sign for addition / using addition instead of subtraction to confuse you. The shepherds start with x sheep. They pay 30 and have x - 30. They should get 5 back, but they only get 3, so they have x - 30 + 3 = x - 27. If the sons had given them the last 2, they’d have x - 27 + 2 = x - 25 = x - 30 + 5.
If you want to view it from the trolls’ side, you need only multiply everything with (-1).
No missing sheep. I’m the end they were supposed to pay 25 but paid 27, so it’s 27 - 2 = 25. 29 and 30 aren’t relevant numbers
Shepards end up with 27, trolls end up with 27. So they must have started with 54.
- 54 // before bridge
- 54 - 3*10 = 54 - 30 = 24 // troll toll
- 24 + 3 = 27 //sons return 3
The troll gets 24, the sons get 3, and the shepards get to keep 27. And since 24 + 3 + 27 = 54 the equation balances.
You’ve had solutions from a few people, so just wanted to chuck in one of my favourite Abbott and Costello sketches with some similarly confusing maths… :-)
As others have stated, there are no missing sheep. Each shepherd “paid” 9 sheep after the discount, 2 are in the hands of the sons, 25 in the hands of the troll.
Or thinking about it in the other direction, 30 were initially transferred, 25 stayed with troll, 2 with sons, 3 back to shepherds.
