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What Must Be True

Thinking Skills · Y4 OC
Year 4 OC
Lesson Guide
Explanation
'Which statement MUST be true?' is asking for the option that is true in EVERY story the facts allow — not just in the most likely story. Three strengths: MUST (true in every allowed story), MIGHT (true in some, false in others — the classic trap), CAN'T (false in all). Facts: 'Rex is a dog.' Then 'Rex is an animal' MUST be true; 'Rex is brown' only MIGHT be; 'Rex is a cat' CAN'T be. Test any option by trying to build a story where the facts hold but the option fails — if you can build one, it's only a might.
Your Turn
Facts: 'Everyone in the choir sang at assembly. Lena is in the choir.' Which MUST be true: Lena sang at assembly / Lena likes singing? Check: Lena sang (forced). Liking singing is only a might.
Watch Out
Likely is not must. An option can be 99% sensible and still be wrong — one allowed story where it fails kills it.
Explanation
When one fact is unknown, split into CASES. Example: three torches in a line, each green or orange; a signal passes from the first (green) to the middle, then from the middle to the last (orange). The middle torch is unknown — so try both. Case 1, middle green: the middle (green) signals the orange last torch — a green signals an orange. Case 2, middle orange: the first (green) signals the middle (orange) — again a green signals an orange. 'A green torch signalled an orange torch' survives BOTH cases, so it must be true. Every other option dies in one of the cases. Cases turn a foggy puzzle into two tiny certain ones.
Your Turn
Ali is older than Ben; Ben is older than Cy OR the same age. MUST 'Ali is older than Cy' be true? Check: yes — both cases (Ben older than Cy / Ben equal to Cy) still put Ali above Cy.
Watch Out
Check EVERY case before crowning an answer — an option that feels right often fails in exactly one case.
Explanation
If-then rules chain. OC style: 'If Ines does not play, Jai will play. If Ines does play, Kai plays instead of Lou.' Given: Jai does NOT play. Step 1: could Ines be out? No — Ines out forces Jai in, and Jai is out. So Ines PLAYS. Step 2: Ines playing fires rule 2 — Kai in, Lou out. Answer: Ines and Kai. Two habits: run rules in the direction that's forced (if the result of a rule is blocked, its trigger is blocked too), and write down each certainty as you earn it — chains are easy on paper, slippery in your head.
Your Turn
Rules: 'If it rains, sport is inside. If sport is inside, the hall is booked.' It rains. What MUST be true? Check: sport inside AND the hall booked — the chain fires twice.
Watch Out
'If A then B' + 'B happened' proves nothing about A. Chains only run forwards — or backwards when an outcome is BLOCKED.
Explanation
Number deductions turn on the exact words 'at least', 'exactly' and 'at most'. Facts: 24 students, everyone plays at least one of chess or checkers, 15 play chess. The 9 students not playing chess MUST play checkers — so 'at least 9 play checkers' must be true. But 'exactly 9' is only a might: chess players may ALSO play checkers, pushing the count anywhere up to 24. When an option states a number, ask: is this forced, or just the smallest possibility? The forced version usually wears 'at least' — the trap wears 'exactly'.
Your Turn
30 tickets sold, adults and children only, 18 to adults. What MUST be true — 'exactly 12 children' or 'at least 12 tickets went to children'? Check: exactly 12 — each ticket goes to one buyer type, no overlap here! Overlap is what made 'exactly' fail before.
Watch Out
Overlap is the whole game: when categories can share members, 'exactly' fails; when they can't, subtraction gives exact answers.
Explanation
The toolkit: (1) STORY TEST — try to build a story where the facts hold but the option fails; success means it's only a might. (2) CASE SPLIT — unknown fact? Run every case; the answer survives all of them. (3) CHAIN RULES — write each forced fact; a blocked outcome blocks its trigger. (4) MIND THE OVERLAP — 'at least' is usually forced, 'exactly' needs no-overlap. In the test you get about a minute: eliminate breakable options quickly, and the unbreakable one is your answer. Quiz and exercises!
Your Turn
Facts: every bird in the cage is yellow or green; there are 5 birds; at least one is yellow. MUST 'there are at most 4 green birds' be true? Check: yes — at least one yellow leaves at most 4 spots for green.
Watch Out
Don't pick the most INTERESTING option — pick the unbreakable one. Must-be-true answers are often the most boring sentence on screen.
📌 Key Points — this lesson in a nutshell
  • MUST = true in every story the facts allow; MIGHT = true in some; CAN'T = true in none. The test wants MUST.
  • Story test: if you can invent one allowed story where the option fails, it is only a might.
  • Unknown fact → split into cases; the answer survives every case.
  • If-then chains run forwards; a blocked outcome blocks its trigger — write each forced fact down.
  • 'At least' deductions are forced by subtraction; 'exactly' fails whenever categories can overlap.
  • The must-be-true answer is often the most boring option — unbreakable beats interesting.
Step 1: Introduction
Step 1 of 5
Three strengths of truth MUST be true true in EVERY story the facts allow the answer they want MIGHT be true true in some stories, false in others a trap option CAN'T be true false in every story a different trap Facts: "Rex is a dog." MUST: Rex is an animal. MIGHT: Rex is brown. CAN'T: Rex is a cat.
Green signals middle, middle signals orange First torch GREEN, last torch ORANGE, middle unknown → two cases: Case 1: middle is GREEN green→green, then GREEN signals ORANGE ✓ Case 2: middle is ORANGE GREEN signals ORANGE first ✓ In BOTH cases, somewhere a green torch signals an orange torch. So "a green torch signalled an orange torch" MUST be true. "Only one torch was green" survives Case 2 but dies in Case 1 → only might. Method: split the unknown into cases; the answer is what survives EVERY case.
The coach's rules Rule 1: If Ines does NOT play, Jai will play. Rule 2: If Ines DOES play, Kai plays instead of Lou. Given: Jai does NOT play. Who is in the team? Step 1: Rule 1 flipped — if Jai is OUT, Ines can't be out. (Ines out would FORCE Jai in. Jai is out → Ines plays.) Step 2: Ines plays → Rule 2 fires → Kai in, Lou out. Team: Ines and Kai ✓ Chain rule: each certain fact fires the next rule — write down what each step FORCES, nothing more.
"At least" and exact counts Facts: 24 students. Every student plays AT LEAST one of chess or checkers. 15 play chess. MUST be true ✓ "At least 9 play checkers" 24 − 15 = 9 not in chess → all 9 in checkers Only MIGHT be true "Exactly 9 play checkers" chess players may ALSO play checkers Number deductions ride on "at least / exactly / at most". The 9 with no chess MUST play checkers — but overlaps mean checkers could have 9, 12, or even all 24.
The certainty toolkit 🔒 Story test a story where the option fails means it is only a might Case split unknown fact → try every case; keep what survives all Chain the rules write each forced fact; blocked outcome blocks its trigger Mind the overlap "at least" is forced; "exactly" needs no-overlap One question, one minute: eliminate the mights fast — the option you CAN'T break is your answer. Quiz time!
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