Read the set-builder clues, then drop each element into the Venn region where it belongs, or tally exactly how many satisfy the condition.
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How to play
Each puzzle gives a collection of elements and conditions written in set-builder notation over two or three sets. In Sort mode you place every element in its correct Venn region; in Count mode you work out how many elements meet a given rule.
Drag each element into the region (A, B, C, an intersection, or outside) that matches the membership rules.
Switch to Count mode to answer combinatorics-style 'how many' questions instead of sorting.
Use Hint if you're stuck and Check to test your current arrangement.
Satisfy every condition to solve the puzzle.
Controls
Desktop: drag elements between regions with the mouse; click Sort/Count, a difficulty, and Daily/Practice in the bar.
Phone & tablet: drag elements with your finger and tap the buttons, touch is fully supported.
Tips & strategy
Translate each clue into plain membership first: 'in A but not B' is the A-only slice.
Handle intersections last, pin down the unambiguous A-only, B-only and outside elements first.
In Count mode, watch for overlap so you don't double-count elements that belong to two sets.
What you'll learn
Cardinal turns set theory and combinatorics into hands-on Venn-diagram sorting and counting.
Skills: set theory, combinatorics, Venn diagrams, counting
Using the formal notation as the clue is the original demand.
Set-builder notation is compact to the point of being opaque until you have parsed a few, and the Venn diagram is its picture. Three sets is where intuition fails — eight regions, several of which are easy to forget exist — so the diagram stops being decorative.
About Cardinal
Cardinal turns set theory and combinatorics into hands-on Venn-diagram sorting and counting. It's an original, free browser game offering Sort and Count modes, three difficulties, and both daily and practice puzzles.
A free, original browser game on PlayPendium. No download, no install.
