The New Sudoku Players' Forum

[rjamil]

A grand vizier is tasked with collecting a special livestock tax for the Caliph. He arrives at a rural province and purchases exactly 100 animals using a budget of exactly 100 dinars.

The marketplace has fixed, rigid pricing based on the type of livestock:

Each Camel costs exactly 5 dinars.
Each Sheep costs exactly 1 dinar.
Goats are cheap: you get 2 Goats for 1 dinar (meaning each goat costs exactly 1/2 dinar).

The Caliph demands that the vizier must buy at least one of each type of animal, use every single dinar of the budget, and bring back exactly 100 living animals (no fractional animals allowed).

The Problem: Because there are three types of animals but only two strict constraints, this is an indeterminate system. What are the exact whole-number combinations of Camels, Sheep, and Goats that the vizier can purchase to satisfy the Caliph?

R. Jamil

[Hajime]

This one is not that difficult.
x=camel y=sheep z=goat
x+y+z=100 and 5x+y+z/2=100
Substract line 1 from line 2
4x - z/2 = 0 or z=8x
Substitute last in Second
5x+y+8x/2=100 or y=100-9x
Enumerate X from 1 to 11

Code: Select all

x   y  z
1  91  8
2  82 16
3  73 24
4  64 32
5  55 40
6  46 48
7  37 56
8  28 64
9  19 72
10 10 80
11  1 88


[rjamil]

This one is, basically, one of the multiple answers riddle.

And, the above answer is correct with logical reasoning.

R. Jamil