Henry Ernest Dudeney/Modern Puzzles/160 - Going to Church

Modern Puzzles by Henry Ernest Dudeney: $160$

Going to Church

A man living in the house shown as $H$ in the diagram wants to know what is the greatest number of different routes by which he can go to the church at $C$.

The possible roads are indicated by the lines, and he always walks either due $N$, due $E$, or $N.E.$;

that is, he goes so that every step brings him nearer to the church.

Can you count the total number of different routes from which he may select?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Unicursal and Route Problems: $160$. -- Going to Church
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Route & Network Puzzles: $417$. Going to Church