Solve Barn Animal Counts from Total Legs
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Solve Barn Animal Counts from Total Legs
A barn contains ants, cows, and chickens with 570 legs in total. The number of ants is twice the number of chickens, and the number of cows is twice the number of ants. Assuming each ant has 6 legs, each cow has 4 legs, and each chicken has 2 legs, how many ants are in the barn?
Give an integer answer and show the equation that establishes uniqueness.
### What a Strong Answer Covers
- One variable that expresses all three animal counts.
- Correct leg contributions for ants, cows, and chickens.
- An equation equal to 570 and an integer solution consistent with every ratio.
- A substitution check of the final counts.
### Follow-up Questions
- How would you detect that a changed total-leg count admits no integer solution?
- If the cow-to-ant ratio were unknown, what additional observation would make the counts identifiable?
Overview: Solve a barn-count puzzle by expressing chickens, ants, and cows with one variable and balancing their leg contributions. The worked answer derives 38 ants, verifies all ratios and the 570-leg total, and explains why the integer solution is unique.
Read the full Sig Data Scientist interview experience this question came from