Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Facts: "All roses in this garden are red. This flower is a rose from this garden." MUST it be red?
Show worked solution
Yes — the facts force it: garden rose → red.
2 Facts: "Tom is taller than Ali." Option: "Tom is the tallest in the class." Is this a must or a might?
Show worked solution
Might — someone else could be taller than Tom. Build the story, break the option.
3 Which word makes a number deduction safe when groups can overlap: "exactly" or "at least"?
Show worked solution
At least — overlap can raise a count above the subtraction answer, never below it.
Level 2 · Core
4 Rules: "If the bus is late, we miss assembly. We did NOT miss assembly." What MUST be true about the bus?
Show worked solution
Not late — a late bus forces a missed assembly; assembly wasn't missed, so the trigger is blocked.
5 Four counters in a row, each black or white. First is black, last is black, and at least one is white. MUST a white counter be between two other counters?
Show worked solution
Yes — the white counter can only be in position 2 or 3, and both are between neighbours.
6 28 students each chose soccer or art (not both). 17 chose soccer. Exactly how many chose art? (number)
Show worked solution
No overlap → 28 − 17 = 11 exactly.
Level 3 · Challenge
7 Rules: "If Ken plays, Lena plays. If Lena plays, Omar sits out." Ken plays. Does Omar play?
Show worked solution
No — chain: Ken → Lena plays → Omar sits out.
8 25 readers each borrowed at least one of mystery or comedy. 16 borrowed mystery. What MUST be true?
Show worked solution
At least 9 — the 9 non-mystery readers must have comedy, and mystery readers may ALSO have borrowed comedy.
9 Three runners finish a race: Ana before Bo, and Cai not last. Who MUST be last?
Show worked solution
Bo — Ana beats Bo so Ana isn't last; Cai isn't last by the facts; only Bo can be last.