Daily Challenge #221 - The Merchant of York

#challenge

Alcuin of York was an English clergyman and scholar who wrote, among other things, recreational mathematical problems.

One of them goes as follows: A merchant wanted to buy 100 pigs for 100 pence. He told his servant to go and buy them, paying 10 pence for a boar, 5 pence for a sow and 1 penny for two piglets. He also told him to buy at least one of each. How many boars, sows, and piglets must there have been for him to have paid exactly 100 pence for the 100 animals?

In this challenge, you are going to create a function buyPigs that takes two arguments.

amount: both the amount of money to buy animals and the number of animals that must be bought.
specs an object indicating how much the merchant is willing to pay for each kind of animal. It will always have the following structure:
```
  boar: { price: Number, qty: Number },
  sow: { price: Number, qty: Number },
  piglet: { price: Number, qty: Number },
```

The function will find a combination of pigs such that:

There is at least one of each kind of pig
The amount of pigs equals the amount of pennies It will return an object indicating the amount of pigs of each kind that the servant bought. If there is no way to solve it, it will instead return the object { error: 'Purchase not possible' } If there are more than one ways to resolve it, it only needs to return one.

Examples:

const pigs = {
  boar: { price: 10, qty: 1 },
  sow: { price: 5, qty: 1 },
  piglet: { price: 1, qty: 2},
}

buyPigs(100, pigs) => { boar: 1, sow: 9, piglet: 90 }
buyPigs(150, pigs) => { error: 'Purchase not possible' }
buyPigs(300, pigs) => { boar: 3, sow: 27, piglet: 270 }

const pigs2 = {
  boar: { price: 5, qty: 1 },
  sow: { price: 1, qty: 1 },
  piglet: { price: 1, qty: 8 },
}

buyPigs(100, pigs2) => { boar: 7, sow: 61, piglet: 32 }
buyPigs(41, pigs2) => { boar: 7, sow: 2, piglets: 32 }

Good luck!

This challenge comes from SavagePixie here on DEV. Want to propose a challenge idea for a future post? Email yo+challenge@dev.to with your suggestions!

Top comments (3)

Vidit Sarkar • Apr 8 '20 • Edited

Hope I have got the problem right.
Here is a possible Python solution,

# amount : amount of pennies
# pigs : dict according to the structure of specs
#       Example:
#       pigs = {
#           'boar': { 'price': 10, 'qty': 1 },
#           'sow': { 'price': 5, 'qty': 1 },
#           'piglet': { 'price': 1, 'qty': 2}
#       }
def buyPigs(amount: int, pigs: dict) -> dict:
    oneBoarPrice = pigs['boar']['price'] / pigs['boar']['qty']
    oneSowPrice = pigs['sow']['price'] / pigs['sow']['qty']
    onePigletPrice = pigs['piglet']['price'] / pigs['piglet']['qty']

    # i : number of boar he can buy
    # j : number of sow he can buy
    # k : number of piglet he can buy
    for i in range(1, int(min(amount-1, amount/oneBoarPrice))):
        for j in range(1, int(min(amount-1, amount/oneSowPrice))):
            for k in range(1, int(min(amount-1, amount/onePigletPrice))):
                # Given that, the amount of pigs equals the amount of pennies
                # so (i+j+k) == amount
                # And, calculated total price == amount
                if i+j+k == amount == (oneBoarPrice*i + oneSowPrice*j + onePigletPrice*k):
                    return {'boar': i, 'sow': j, 'piglet': k}

    # if no case found then return this
    return {'error': 'Purchase not possible'}

Output,

pigs = {
    'boar': { 'price': 10, 'qty': 1 },
    'sow': { 'price': 5, 'qty': 1 },
    'piglet': { 'price': 1, 'qty': 2}
}

pigs2 = {
  'boar': { 'price': 5, 'qty': 1 },
  'sow': { 'price': 1, 'qty': 1 },
  'piglet': { 'price': 1, 'qty': 8 }
}

print(buyPigs(100, pigs)) # output -> {'boar': 1, 'sow': 9, 'piglet': 90}
print(buyPigs(150, pigs)) # output -> {'boar': 6, 'sow': 4, 'piglet': 140}
print(buyPigs(300, pigs)) # output -> {'boar': 3, 'sow': 27, 'piglet': 270}

print(buyPigs(100, pigs2)) # output -> {'boar': 7, 'sow': 61, 'piglet': 32}
print(buyPigs(41, pigs2)) # output -> {'boar': 7, 'sow': 2, 'piglet': 32}