1. Solve the readers puzzle.
- Place Ben–Rivers. Asha and Cara must take Space and Plants.
- Asha cannot take Space, so Asha–Plants and Cara–Space.
- All three clues hold and no alternative remains.
Maths · Suggested Classes 5–8
World Logic Day 2027: Three Explainable Grid Puzzles
A puzzle can have a neat-looking answer and still lack enough clues. These three challenges ask you to show what must be true—and notice when more than one solution survives.
Start here
World Logic Day is 14 January 2027. Try three original constraint puzzles, including one deliberately underdetermined case, with worked explanations and a puzzle-making record.
Original BananaLearn guide · 7 November 2026
On a narrow screen, swipe the diagram or open it full size.
Find a section, worked example or practice question
Date and what counts as a solution
UNESCO’s World Logic Day is observed on 14 January, so the 2027 date is 14 January 2027. This independent activity supplies original puzzles rather than an official programme or theme.
Allow about 25–40 minutes. Use paper grids or list possible assignments. A correct solution satisfies every clue; a unique solution also requires showing that no other assignment survives.
Puzzle 1: three readers, three books
Asha, Ben and Cara each borrow one different book: Space, Rivers and Plants. Asha does not borrow Space. Ben borrows Rivers. Cara does not borrow Plants. Who borrows each book?
Make a three-by-three grid and mark Ben–Rivers first. A used book cannot be assigned to someone else. Apply each negative clue to eliminate possibilities before filling the remaining squares.
Explain the reader solution
Ben has Rivers, leaving Space and Plants for Asha and Cara. Asha cannot have Space, so Asha has Plants and Cara has Space. Cara’s not-Plants clue is consistent with the result.
For this small puzzle, the Ben clue and Asha clue already determine the assignment. The extra Cara clue checks consistency but is redundant. Redundant does not mean false; it means the clue is not needed for uniqueness here.
On a narrow screen, swipe the diagram or open it full size.
Puzzle 2: three club sessions
Art, Coding and Music each have one different starting slot: 9 am,10 am and 11 am. Coding starts later than Art. Music starts at 10 am. Determine the timetable.
Music occupies the middle slot. The other two slots are 9 and 11, and the order clue forces Art to 9 and Coding to 11. The words later than compare order; they do not mean immediately after in every puzzle.
Puzzle 3: one prize and exactly one true statement
There are Red, Blue and Green boxes, exactly one of which contains a prize. Red’s statement says “The prize is in Blue.” Blue’s says “The prize is not in Blue.” Green’s says “The prize is in Red.” Exactly one statement is true. Can you locate the prize uniquely?
Test each possible location rather than trusting the colour of a box or assuming every puzzle has one answer. Count the true statements in each case.
Find the missing information
If the prize is in Red, the truth counts are false,true,true: two true statements, so reject it. If it is in Blue, the counts are true,false,false: one true, so keep it. If it is in Green, they are false,true,false: one true, so keep it.
Both Blue and Green satisfy the clues. There is no unique location. Adding the clue “The prize is not in Green” would make Blue unique. The important answer is the surviving possibilities and the reasoning, not a forced guess.
Write a puzzle another person can check
Choose a small set of items and slots. Write an intended assignment, then supply clues. List all possible assignments or test them systematically to check uniqueness. Give the puzzle to a reader without revealing your answer.
If two answers survive, add a discriminating clue. If none survives, a clue may contradict another. Do not fix either problem by simply declaring your intended answer correct.
Keep an evidence trail
For every filled grid square, write the clue or elimination that justifies it. For the box puzzle, use a table of candidate location and truth count. A completed grid without explanations hides lucky guesses.
For parent support, ask “which clue rules that out?” rather than giving the next placement. An extension can ask which clues are redundant or how removing a clue changes the number of solutions.
See the reasoning
Worked examples and checks
2. Solve the club timetable.
- Music is fixed at 10. Art and Coding must use 9 and 11.
- Coding is later than Art, so Art–9 and Coding–11.
- The timetable uses each slot once and obeys the order clue.
3. Why does the prize puzzle have two solutions?
- Red’s and Blue’s statements are opposites, so exactly one of those is always true.
- To keep the total at one, Green’s statement must be false; the prize is not in Red.
- Nothing else distinguishes Blue from Green, so both survive.
Try, explain, check
12 questions with explained answers
Try each task before opening its explanation. These are original BananaLearn questions, not official exam or past-paper questions. Where several answers can work, the explanation gives the criteria.
What is the 2027 observance date?
Check answer and reasoning
14 January 2027
It is UNESCO’s annual 14 January observance.In Puzzle 1, who has Rivers?
Check answer and reasoning
Ben
The clue states it directly.Who has Plants?
Check answer and reasoning
Asha
Ben uses Rivers and Asha cannot have Space.Which reader clue is redundant after the others determine the assignment?
Check answer and reasoning
Cara does not have Plants
The same unique solution follows without it.In Puzzle 2, when is Music?
Check answer and reasoning
10 am
It is explicitly fixed.When is Coding?
Check answer and reasoning
11 am
Music uses 10 and Coding must be later than Art.Does later always mean immediately later?
Check answer and reasoning
No
It specifies an order unless a clue adds adjacency.How many statements are true if the prize is in Red?
Check answer and reasoning
2
Blue’s and Green’s statements are true.Which prize locations survive?
Check answer and reasoning
Blue and Green
Each gives exactly one true statement.Give one additional clue that selects Blue.
Check answer and reasoning
The prize is not in Green
It removes the other surviving location.What does no surviving assignment suggest?
Check answer and reasoning
The clues may be inconsistent
Check for a contradiction or a mistaken interpretation.Does one valid assignment prove uniqueness?
Check answer and reasoning
No
You must exclude the alternatives too.
A checking record to use in your notebook
Copy these headings and fill them for one worked task, then for a fresh attempt. Use your own evidence rather than copying the model answer.
- Date and setting
- What is confirmed, and which example is fictional?
- Task and conditions
- Which rule, quantity, passage or clue is supplied?
- Plan or answer
- What will I calculate, say or change?
- Evidence
- How can another reader check the reasoning?
- Revision
- What would I change after a trial or rehearsal?
Choose the next useful step
- Explain reasons and challenge assumptions
- List possibilities systematically
- Turn an instruction sequence into an algorithm
Explore BananaLearn’s games, learning features and one-to-one tutoring. Maths is our priority; English and Science tutoring are also available. Bring a recent example of schoolwork when checking teaching fit.
Sources, level and update
Original BananaLearn explanations, examples, illustrations and practice. Source facts checked 7 November 2026. Suggested levels are learning guides, not a claim that every board or textbook uses the same sequence.
Event timing is calendar-backed. Search demand is a forecast unless a separately measured trend is stated. No official event theme, school programme or affiliation is implied.
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