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 The mystery number is 3, 5 or 7. Fact: "it is not 3 and not 7." Is the outcome settled?
Show worked solution
Yes — only 5 survives.
2 The mystery number is 3, 5 or 7. Fact: "it is bigger than 4." Settled?
Show worked solution
No — 5 and 7 both survive. Narrowed is not settled.
3 Which three words most often mark a settling option: only, every, and ____?
Show worked solution
'Only', 'every', 'none' — the totality words.
Level 2 · Core
4 Pet is a cat, dog or rabbit. Fact: "the pet does not bark and has long ears." Assume only dogs bark and only rabbits have long ears. Settled — and to what?
Show worked solution
No bark removes dog; long ears force rabbit. Settled.
5 Score is 1-6 (a dice). Fact A: "even". Fact B: "greater than 4". Do A and B TOGETHER settle it?
Show worked solution
Yes — even and >4 leaves only 6.
6 Winner is Ana, Ben or Cy. Fact: "Ana beat Ben." How many possible winners remain? (number)
Show worked solution
2 — Ana or Cy. Ben is eliminated, but the fact doesn't order Ana and Cy.
Level 3 · Challenge
7 Everyone cast 2 votes for 2 DIFFERENT animals out of rabbit/fish/lizard. Can any student have voted fish twice?
Show worked solution
No — two votes must be different animals. This stem fact powers the class-pet vote puzzle.
8 A pet is bought only if EVERY student voted for the same one animal. 2-different-votes each. Is buying a pet ever possible with 3 animals and 2 votes each? Think: each student names 2 of 3 animals; for fish to be unanimous every student must include fish. Possible in principle?
Show worked solution
Yes in principle — every student could pair fish with something. That is why extra facts are needed to settle the question.
9 Stem: "the secret card is a heart or a spade; hearts are red, spades are black." Option 1: "the card is not red." Option 2: "the card is a picture card." Which option number settles the suit? (1 or 2)
Show worked solution
Option 1 — not red eliminates hearts, leaving spade. Picture cards exist in both suits: idle fact.