Have Chocolate, Will Travel

Algebra Level 3

A traveler visits each point \((x,y) \) with integer coordinates where \(0\leq x,y \leq 4\) (each blue dot in the picture). At each of these points \((x, y)\), the traveler eats \[\frac {1}{2\max\{x,y\} + 1}\]

chocolate bar(s). How many chocolate bars will the traveler eat in all?

Notation. \(\max\{x,y\}\) represents the largest value in the set \(\{x,y\}\).

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