What must be true
Name: Date:
1. Challenge puzzlesFind how many four-legged animals. Show how you worked it out.1 question
1A pet shop keeps 19 parrots and cats. Altogether they stand on 68 legs.How many are cats?Why
- Free
- Grades 4–6
- 4 sections · 4 questions
What must be true
Four questions that look like they are missing something — and are not.
- Answer key on its own page
- Reopen this exact paper
- Letter & A4 ready
Ready to printWhat must be true
The answer key prints on a separate page.
What's on this test
Each section hands over fewer facts than there are unknowns, which is normally the definition of an unanswerable question. Each is rescued by something the situation refuses to allow. Animals have two legs or four, never three. Nobody buys two thirds of a pen. Three shares described against one another are not three mysteries but parts of one. And on the island, a liar's false words pin a thing down exactly as a truth-teller's true ones do, so three unknown KINDS are settled by nothing but what each person says. None of these is an extra fact you are given; they are facts you notice.
How the paper is put together
That is why the sections sit in this order: two unknowns with two facts, then two unknowns with ONE fact and whole items doing the rest, then three unknowns and a single total, and last the islanders, whose only facts are three sentences. The amount a child has to hold in their head grows, while the arithmetic underneath stays inside what they already know — the final section has no arithmetic in it at all.