How do you build the longest-span stick bridge?

Short answer: some contests score the greatest gap crossed, not the strongest bridge. The usual approach is to reach out from both sides as far as you can without tipping, then meet in the middle, using the weight of the stick pile and clever overlaps. Check the exact rules first, since they vary.

An example of this kind: a fixed number of craft sticks and a length of tape, the bridge must support a small mass for a few seconds, the supports are moved apart, and the longest gap wins.

Ideas to try

1. Overlap sticks like shingles. The more overlap, the more each stick is held by the ones around it.
2. Think cantilever. A cantilever sticks out from a support. Its own weight tries to tip it over, so it needs anchoring weight behind the support.
3. Anchor with the stick pile. Stack sticks behind the supports to counterbalance the reach.
4. Keep the center of gravity over the supports until the two halves meet.
5. Reduce weight at the tips. Lighter ends can reach farther.
6. Use tape where it counts, at the middle, to tie the halves together.

Practice

Build many small tests, and measure the longest span each held. Change one thing at a time. The best designs usually come from tests, not drawings.

Also check what the rules say about the load, the supports and ties. See how contests score entries and reading your rulebook.