Day 7 - Lamar Valley

You drive over to the Lamar Valley to see the bison and elk herds. When you arrive, the animals have scattered across the landscape and are not arranged in herds. The bison cows have all been separated from their calves!

You need to figure out how far the cows will have to travel to retrieve their calves. You can map out the location of the cows and their calves using a grid, where each cell is 50 yards wide and 50 yards long. Unfortunately, the cows can only move horizonatally or vertically across the valley, so the shortest distance between a cow and her calf is the Manhattan distance between them. Each cow/calf pair is designated by a upper/lowercase letter pair. For example, the cow is ‘A’ and the calf is ‘a’.

This small map shows two cow/calf pairs.

**********
*..A.....*
*......b.*
*........*
*.B......*
*........*
*........*
*.....a..*
*........*
**********

The distance between cow A (at row 2, column 4) and calf a (row 8, column 7) is 9. The distance between cow B and calf b is 7. The total distance is (9 + 7) * 50 = 800 yards.

You can see 26 cow/calf pairs. How far will the cows need to travel find their calves?

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