---
type: "problem"
title: "A cow issue"
slug: "a-cow-issue"
author: "sequoia"
tags: ["matrices", "rank", "system"]
difficulty: 47
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

You are a farmer and your field contains $2n+1$ cows where $n\geqslant 1$.

For all choice of two distinct groups of $n$ cows, you observe that the total mass of each group is the same.

Show that all your cows have the same mass.