","content":"Let's first build the branches where the **first digit is 1**.\n\nIf the first digit is **1**, the remaining cards are **6, 6, 7**.\n\n* **First digit:** $1$\n * **Second digit:** Can be either $6$ or $7$.\n * **If second digit is $6$:** The remaining cards are $6$ and $7$.\n * **Third digit $6$** $\\rightarrow$ **Fourth digit $7$** $\\rightarrow$ Number: **1667**\n * **Third digit $7$** $\\rightarrow$ **Fourth digit $6$** $\\rightarrow$ Number: **1676**\n * **If second digit is $7$:** The remaining cards are $6$ and $6$.\n * **Third digit $6$** $\\rightarrow$ **Fourth digit $6$** $\\rightarrow$ Number: **1766**\n\nThis gives us our first **3** numbers:\n$$\\text{1667, 1676, 1766}$$"},{"type":"text","order":2,"title":"Branch starting with 6","content":"$43"},{"type":"text","order":3,"title":"Branch starting with 7","content":"Finally, let's build the branches where the **first digit is 7**.\n\nIf the first digit is **7**, the remaining cards are **1, 6, 6**.\n\n* **First digit:** $7$\n * **Second digit:** Can be $1$ or $6$.\n * **If second digit is $1$:** The remaining cards are $6$ and $6$.\n * **Third digit $6$** $\\rightarrow$ **Fourth digit $6$** $\\rightarrow$ Number: **7166**\n * **If second digit is $6$:** The remaining cards are $1$ and $6$.\n * **Third digit $1$** $\\rightarrow$ **Fourth digit $6$** $\\rightarrow$ Number: **7616**\n * **Third digit $6$** $\\rightarrow$ **Fourth digit $1$** $\\rightarrow$ Number: **7661**\n\nThis gives us the final **3** numbers:\n$$\\text{7166, 7616, 7661}$$"},{"type":"text","order":4,"title":"Summarize the complete list","content":"By combining all branches of our tree, we find a total of **12** different possible numbers:\n\n* **Starting with 1:** 1667, 1676, 1766\n* **Starting with 6:** 6167, 6176, 6617, 6671, 6716, 6761\n* **Starting with 7:** 7166, 7616, 7661\n\n### Markscheme Guidance:\n* Award **1 mark** if you write down at least 4 correct numbers. M1\n* Award **2 marks** if you write down at least 8 correct numbers. M1\n* Award **3 marks** if you list all 12 correct numbers. A1"}]}],"generatedAt":"2026-06-12T15:22:32.255Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"833dfef1-f444-4019-b7f3-e79fea545630","revisionId":"e15fecbb-257f-4dae-8955-3d201de036d7","questionNumber":null,"questionType":"LA","specification":"Mia is planning a day trip. She chooses one method of transport and one destination from the options below.\n\n| Transport | Destination |\n| :--- | :--- |\n| Train | London |\n| Bus | Bristol |\n| Car | Cardiff |","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"ce169e76-a61a-4c13-9fcf-9b0dd64bb029","label":"a","content":"Write down all the possible combinations of transport and destination Mia can choose.","markscheme":"- Train + London, Train + Bristol, Train + Cardiff\n- Bus + London, Bus + Bristol, Bus + Cardiff\n- Car + London, Car + Bristol, Car + Cardiff\n\nAward 1 mark for at least 4 correct combinations. M1\nAward 2 marks for all 9 correct combinations. A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"At least 4 correct combinations identified.","code":"M"},{"id":"p2","marks":1,"description":"All 9 correct combinations identified without repeats.","code":"A"}],"finalAnswers":["Train + London, Train + Bristol, Train + Cardiff, Bus + London, Bus + Bristol, Bus + Cardiff, Car + London, Car + Bristol, Car + Cardiff"],"generatedAt":"2026-05-06T13:59:07.179Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"systematic_listing","label":"Systematic listing","steps":[{"type":"text","order":0,"title":"Choose a fixed order","content":"List the destinations in the same order for each transport: London, Bristol, then Cardiff. This systematic order helps you avoid missing or repeating a combination.","highlights":[{"text":"one method of tr

Systematic Listing

Question 19

Systematic Listing Questions

Systematic Listing

Question 19

Systematic Listing Questions