Ivan Shishkin, Rye (1878)

Problems/OtherUnreviewed

Nar-mayas and the caravan master

by Ancient Tree·
16
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
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Nar-maya are female hybrids born from a female camel and a male dromedary. Unlike the camel, which has two humps, and like the dromedary, a nar-maya has one hump.
image
A camel (left) and what could be either a dromedary, or a nar-maya (right). You have no idea because they really look alike.

You want to acquire as many dromedaries as possible for their milk, but absolutely no nar-maya, because they do not produce tasty milk and are very difficult to sell.
If you buy camels, that’s fine, because they can’t be confused for anything else, so they are way easier to sell.

A caravan master offers you his herd. His condition: "If you buy from me, you buy the whole herd. Not one animal less." His offer is very tempting.

You go to inspect the animals. They stand behind a low wall: the humps rise above it, but nothing else is visible.
camel
You count 13 humps. However, you cannot determine exactly how many animals there are.

A child runs at you and innocently explains: "These are the mothers with their calves (their children). Each mother of the herd had exactly one calf. The males are kept in another enclosure."

You turn to the caravan master: "Were any of the calves nar-maya?"

The caravan master says: "A few, but we have sold every nar-maya yesterday, together with its mother".
He quickly adds: "Of course, we always sell a calf and its mother together, as the sacred laws of our country command".

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Solution by Ancient Tree

Discussions0 useful votes

You should decline the offer, as the caravan master is lying somewhere.
Indeed, there are as many mothers as calves (because each mother had one calf, and the caravan master said they were only sold together).
For each pair "mother + calf", there are two options if we exclude nar-maya:

  • The mother is a camel, the calf is a camel →\rightarrow that makes 2+2=42+2=4 humps.
  • The mother is a dromedary, the calf is a dromedary →\rightarrow that makes 1+1=21+1=2 humps.

So, if there are no nar-maya, there should be an even number of humps. But 1313 is not even!

So either the caravan master is lying about there not being nar-maya, or about never selling a calf without its mother. So you cannot safely take his offer!

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