Some of DiscreteQuest’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
Teach Tally the Pattern-Counter
You be the teacher — Tally the Pattern-Counter is still learning. Helping Tally the Pattern-Counter figure it out is the practice. (Only for you; nothing is saved.)
To count students taking Art OR Music without double-counting, what do you subtract?
Sortie then says: “20 take Art, 15 take Music, so 35 take Art or Music — just add them.” — is that right?
The link: Tally's inclusion-exclusion IS Sortie's set operations put to work counting.
Now they see it: counting without over-counting is a set-operations problem in disguise.
Tally (counting principles (the multiplication rule)) ×Marshal (permutations (arrangements where ORDER matters))
Why does arranging 4 books in a row give 4 × 3 × 2 × 1?
Tally then says: “4 books in a row: 4 arrangements, one per book.” — is that right?
The link: a permutation is Tally's multiplication rule walking down an ordered line of choices.
Now they see it: "how many orders?" is just the counting rule, one slot at a time.
Wander (graph theory (vertices connected by edges)) ×Swatch (graph coloring (neighbors must differ, fewest colors))
In graph coloring, what decides which two regions are NOT allowed to share a color?
Wander then says: “Two regions can share a color as long as they're roughly the same shape.” — is that right?
The link: Swatch's coloring lives inside Wander's world — the graph's edges ARE the coloring constraints.
Now they see it: coloring a map is really coloring a graph — regions are vertices, borders are edges.
Capstone — plan the chess tournament
You're organizing a chess tournament. Each part below needs ONE of the cast's ideas — bring in the right person for each.
List all the players entered as one collection.
Who do you bring in?
Count how many total games if everyone plays everyone once.
Who do you bring in?
Arrange the top 3 finishers on the podium — gold, silver, bronze.
Who do you bring in?
Draw who-plays-who as dots joined by lines.
Who do you bring in?
Assign time-slots so no player has two games at once.
Who do you bring in?
Notice what you just did: no single idea ran the tournament — you PICKED the right idea for each step and connected them. That's what knowing discrete math really means.
The whole cast, working together — because you taught each one and saw how they fit.
Each idea is a person you teach. A filled circle is one you can teach; a solid line is a connection you've taught. Fill the map by teaching the cast + their connections.
