How the activities are made

The rules, in the order they run

1. The question list

1. Rows. Each row is a question (1 to 160 characters), its answer (1 to 60) and up to 3 wrong answers. Empty rows are skipped. A row with something missing or too long says what, and nothing is made until it is fixed or removed. Text is never cut short.
2. Count. The activities need 4 to 40 questions.
3. Same answers. Two answers that a student could not tell apart count as the same: capitals, spaces and the way a number is written do not matter, so 0.5, .5 and 1/2 are one answer, and 12 cm and 12cm are one answer. Two questions with the same answer get a note on both rows.
4. Maths on the sheets. A slash between two whole numbers (3/4) is set as a stacked fraction, a caret raises what follows it (x^2, 10^-3, 2^(n+1)), and an asterisk or an x between two numbers is set as the multiplication sign. Everything else, units included, prints as typed.

2. Wrong answers

The wrong answers you type come first, in your order. Then, if you allow it under the list, the maker writes more. For an answer that is one number, with any unit or sign kept exactly as you typed it, the rules run in this order:

1. Off by one in the last written place: 41 and 43 for 42, 0.24 and 0.26 for 0.25, 2/4 and 4/4 for 3/4 (the bottom number kept).
2. The sign flipped, only when the answer is negative or the question has a minus sign in it.
3. A mixed up operation, when the question is two numbers joined by one operation: added instead of multiplied and the other way round, added instead of taken away, multiplied instead of divided, a power worked as a product (7^2 as 14), and two fractions added or taken away top and bottom (1/2 + 1/4 as 2/6).
4. A place value slip, for whole numbers and decimals: ten times the answer and a tenth of it, written as a student would (25 kg for 2.5 kg, not 25.0 kg), with at most one more decimal place than the answer. Fractions get none.
5. Off by two, then three, when more are needed.

For a word answer, when you choose wrong answers for words too, the rules make spelling near misses of its longest word: two neighbouring letters swapped, a letter doubled or a double letter written once, and a vowel changed. Every made or typed wrong answer that is the same as its own answer, as the correct answer to any other question in the list, or as a wrong answer already kept, is dropped. So a wrong answer can never be right somewhere else on the sheet.

3. The maze

1. The grid. Squares (each touches 4 others) or hexagons (each touches 6), from 4 by 4 to 8 by 8. The automatic size is the smallest that leaves at least 2 in 5 boxes off the path. Squares hold up to 40 questions, hexagons up to 35.
2. The path. One box more than there are questions, from Start to Finish, chosen at random from the maze code. It never touches itself: two path boxes touch only when they are next to each other on the path.
3. The path boxes. Start holds question 1. Each box after it holds the answer to the question before it and the next question, in list order. Finish holds the last answer.
4. The other boxes. Each box touching the path shows a wrong answer, if possible one written for the question next door, and the boxes around one path box all show different answers. Every box off the path also shows a question from the list, used again (a box off the path is never on the key route), chosen so that none of the boxes it touches shows its answer or any likely wrong answer to it: your typed ones and every one the rules above make, before any is dropped for being another question's answer. It is a dead end for a right answer and for a likely slip alike.
5. The check. Before a maze is shown, it is searched route by route, never visiting a box twice: every route that takes one wrong turn to any box and then answers correctly, and every route that at each box gives the right answer or any likely wrong answer, as many times as it likes. Only the key path may reach Finish. A maze that fails is never shown: the maker tries again with new choices, then a larger grid. For a short list whose answers sit very close together (1, 2, 3, 4), the off by two and three fillers are let through when nothing else works; if even that fails, the page says to add questions with different answers or more varied wrong answers.

The result: a student who answers correctly always has exactly one box to move to. After a wrong turn, the next answer is not next to the student, so the only way on is back one square, onto the path, which the student page says in one line: “If your answer is not next to you, go back one square and check your work.” The page also says how many boxes the path has. A student who moves at random can still reach Finish, as in any maze; the key shows the path to mark against. Two answers two steps apart on the path must differ, or the box between them would show the same answer twice; the page says so if they do not.

4. The riddle decoder

1. The message has 5 to 80 letters, digits and spaces, printed in capitals.
2. Repeated letters, your choice: every blank its own question (one question for each letter of the message), or every blank of one letter sharing a question (one question for each different letter). The questions are used from question 1 in list order; which one goes to which blank is shuffled from the decoder code.
3. The bank holds every answer used, each with its letter, and the first wrong answer of each question used, each with another letter from the message. It is shuffled from the code.
4. The check. Every answer used is in the bank exactly once, no two bank entries are the same answer, and a student who answers every question correctly spells the message exactly.

5. The card loop

1. The cards. One card per question. In loop order (the list order, or mixed from the card code) card 1 is the START card: it asks question 1 and has the last answer. Every other card has the answer to the question before it and asks its own.
2. Every answer different, or two cards would both say I have. The page names any questions that share an answer.
3. The check. Following Who has from the START card visits every card once and comes back to START.
4. The sheets. 6 or 8 cards a sheet with dashed cut lines. Blank cards, if you keep them on, fill the last sheet and say they are not in the game. Each card has a number in its corner, shuffled, so the numbers do not give the order away.

6. Printing

Every sheet is laid out on A4 or US Letter with half inch margins, and the same layout feeds the preview, the PDF, the picture and the printed page. Text is set at the largest size that fits and never cut: a maze answer too wide for its box goes one step smaller, then onto two lines; when a maze still does not fit, each box shows its question number and the questions are listed on the next page. The maze code, the decoder code or the card code is printed on each sheet; the same list, settings and code always give the same sheet.

Worked example: times tables: 6 to 9

The 10 questions of the times tables example (see the examples), with no wrong answers typed, so every wrong answer below comes from the number rules.

The maze. 5 by 5 squares, with a path of 11 boxes from Start to Finish. Maze code 0005YV. The path, from Start: question 1 is answered by 42, then 56, then 54, then 64, then 49, then 72, then 36, then 81, then 48, then 63, which is in the Finish box.

The riddle decoder, with the message “Great work” and every blank its own question: 9 blanks from 9 questions, 18 answers in the bank (9 of them wrong). Question 10 is not needed. Decoder code 0005YW.

The card loop, in list order: 10 cards and 2 blank cards on 2 sheets of 6. Card code 0005YX. The START card asks 6 × 7 and has 63, the answer to the last question.

What it is not

• Not a marker. It checks that each activity works as a puzzle; it cannot know whether an answer you typed is right. Check the keys.
• Not a question bank. Apart from the six examples, every question is yours.
• Not proof against random moves. The maze stops right answers and likely slips from going anywhere but the path; a student who moves at random can wander, as in any maze.
• Not a diagnosis. Wrong answers made by the rules are common slips, not a judgement of why a student went wrong.
• Not an uploader. Everything happens in your browser, and nothing you type is sent anywhere.

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