# Arabella’s Spider Web

A puzzle by National Security Agency mathematician Katrina J., from the agency’s September 2017 Puzzle Periodical:

Problem:

Arabella the Spider is saving food for the long winter. Arabella wants to store the bugs she caught on 26 fallen leaves, so she can find them later. But, Arabella doesn’t want to waste time by going through any leaves more than once.

In Arabella’s original web, Arabella can’t get to all of the leaves without crossing some of them more than once. But, if Arabella adds just one web between two of the leaves, she can get to every leaf without repeating. [NOTE: The NSA image shown here contains an error — there should be an additional strand between leaves 4 and 22.] There are four different pairs of leaves that Arabella could connect to solve her problem. Can you find all four possible solutions?

Note: Arabella may take any path she chooses as long as she begins on leaf 1 and ends on leaf 26.

Bonus Puzzle:

Can you show why Arabella cannot get to every leaf without repeats on her web as it is now?