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Determine a Canoe Departure Time

SIG (Susquehanna)Data Scientist · Online Assessment
EasyData ScientistOnline AssessmentStatistics & Math

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This problem tests algebraic modeling and systems of linear equations by requiring the candidate to derive the counts of different entities based on a total sum constraint.

The Farmstead Riddle

You are visiting a farm containing only ants, chickens, and cows. You observe the following information:

  1. Every ant has 6 legs, every chicken has 2 legs, and every cow has 4 legs.
  2. The total number of legs observed in the barn is 570.
  3. The number of ants is exactly twice the number of chickens.
  4. The number of cows is exactly twice the number of ants.

Given these constraints, calculate the total number of ants present in the barn.

Example

If there were 1 chicken, there would be 2 ants (twice the chickens) and 4 cows (twice the ants).

  • Legs calculation: (1 * 2) + (2 * 6) + (4 * 4) = 2 + 12 + 16 = 30 legs.
  • Based on the total of 570 legs, you must determine the specific multipliers that satisfy the leg count provided.

Constraints

  • The number of each animal must be a positive integer.
  • All conditions regarding relative populations must be strictly satisfied.

Hints

Hint 1

Define the number of chickens as a variable 'x' and express the number of ants and cows in terms of 'x'.

Hint 2

Create an equation representing the total sum of legs: (Number of Chickens * 2) + (Number of Ants * 6) + (Number of Cows * 4) = 570.

Hint 3

Substitute your expressions from the first hint into the leg equation to solve for 'x', then multiply by two to find the ant count.

Follow-up questions

  • If the number of legs was unknown, but you were told the total number of animals was 105, how would your approach change?
  • How would the solution change if we discovered that some of the ants had lost a leg due to a scuffle?
  • If you were writing a program to solve this for any number of legs N, what complexity would your algorithm have?