Teaching logic, sets and binary with a 16-piece game
Quads has 16 pieces, and each is tall or short, dark or light, round or square, and solid or hollow. Those four yes-or-no traits give exactly 24 = 16 combinations, one piece each. That makes the set a hands-on model for sorting by attributes, Venn and Carroll diagrams, logical "and / or / not", and 4-bit binary numbers. The game itself trains careful reasoning, because you win by not handing your opponent a piece that completes a line.
Why this set of pieces is so useful
Most attribute sets used in classrooms, like attribute blocks, have uneven categories: three shapes, two sizes, several colours. Quads pieces are perfectly balanced. Every trait splits the set exactly in half, and any two traits split it into four groups of four. That regularity makes patterns easy to see and to talk about.
The game was designed around the same idea. In Quarto, the classic game that uses this mechanic, the inventor Blaise Muller was a mathematician. Quads is an independent take on it that you can play free on a phone, tablet or laptop.
Activity 1: Sort and describe (ages 7+, 10 minutes)
Goal: name attributes precisely and see that one object can belong to many groups.
- Show all 16 pieces (on screen, or with a physical set).
- Ask students to sort them into two groups any way they like, then name the rule ("dark ones and light ones").
- Challenge: find a different rule that also makes two groups of eight. There are exactly four such rules, one per trait.
- Hold up one piece and have students describe it completely using exactly four words. Every piece needs all four words, and no two pieces share the same description.
Discussion: why do four words always identify a piece uniquely? (Because there's exactly one piece for each combination.)
Activity 2: Venn and Carroll diagrams (ages 8+, 15 minutes)
Goal: practise intersection, union and complement.
- Draw two overlapping circles labelled tall and dark.
- Place all 16 pieces. Students should find exactly 4 in the overlap (tall and dark), 4 only in "tall", 4 only in "dark", and 4 outside both.
- Ask: how many are tall or dark? (12.) How many are not tall? (8.)
- Redraw as a 2×2 Carroll grid (tall / short across, dark / light down). Same four groups of four, just arranged differently.
- Harder: add a third circle, hollow. How many pieces are in the centre where all three overlap? (2: the round and square versions.)
Activity 3: Every piece is a 4-bit number (ages 10+, 20 minutes)
Goal: connect binary place value to something physical.
Give each trait a place value, and score 1 if the piece has the first version or 0 if it has the second:
| Trait | Place value | 1 means | 0 means |
|---|---|---|---|
| Height | 1 | tall | short |
| Colour | 2 | dark | light |
| Shape | 4 | square | round |
| Fill | 8 | solid | hollow |
Add up the place values of a piece's "1" traits to get its number. For example, the tall dark round hollow piece is 1 + 2 + 0 + 0 = 3, or 0011 in binary. The short light round hollow piece is 0, and the tall dark square solid piece is 15, or 1111.
- Have students number all 16 pieces. They should get every number from 0 to 15 exactly once. The 16 pieces above are in that order.
- Ask: which two pieces are "opposites"? (Pairs that add to 15, like 3 and 12, differ in every trait.)
- This isn't just a classroom trick. It's how the Quads app stores pieces: each is a number from 0 to 15, one bit per trait.
Extension for older students: four pieces share a trait if some bit is 1 in all four, or 0 in all four. Programmers check this with a bitwise AND of the numbers, and an AND of their inverses.
Activity 4: Play, then justify (ages 8+, 20–30 minutes)
Goal: logical reasoning out loud, including negation ("this piece is safe because it is not dark").
- Teach the rules in two minutes with the illustrated rules page. Four pieces in a row, column, diagonal or 2×2 square that share any one trait win, and your opponent chooses the piece you place.
- Pair students up with one device in Pass & Play mode.
- Add one classroom rule: before handing over a piece, say why it's safe, for example "Row 2 is all dark, and this piece is light, so it can't win there."
- Wrap up by asking what made the last few moves harder than the first few. (More lines with three matching pieces means fewer safe pieces.)
For a shorter, self-checking version, use the daily puzzle. Each one has a single right answer and resets on a wrong move.
Practical notes for classrooms
- Devices: the free app runs on iPhone, iPad and Android, and there's a browser version for laptops and Chromebooks.
- No accounts: students don't sign up or log in, and the app has no chat or online play with strangers.
- Ads: the free app and the browser version show ads. A one-time in-app purchase removes them in the app. See the privacy policy for what's collected.
- Offline: the app works without an internet connection once installed.
- Physical sets: you can also run activities 1–3 with any 16-piece, four-trait set, including a classic Quarto board game, or with paper cut-outs.
Independence note: Quads is an independent game. It isn't made by, affiliated with, or endorsed by the makers of Quarto.