Editorial self-study SET for 2027; not an official SASMO 2027 examination. Known source years remain in individual attributions. Time: 90 minutes. Platform scoring starts at 0: Q1–15 are worth 2 points each; Q16–25 are worth 4 points each; wrong and blank answers score 0; maximum 70. Official SASMO scoring instead starts at 15, deducts 1 for an incorrect Section A answer and has a maximum of 85. Verified means editorially checked; assumptions, source errors and mathematical uncertainty are disclosed where relevant.
A soccer match has two 45-minute halves with a 15-minute break between them. It begins at 1:00 p.m. and has no extra or added time. At what time does it end? Enter a 24-hour time as HH:MM.
The operator $\Delta$ gives $3\Delta2=15$, $4\Delta4=24$, $5\Delta9=42$, and $6\Delta1=21$. What is $2\Delta7$?
Pattern convention: use a simple common arithmetic rule consistent with all four examples; the examples alone do not determine a unique arbitrary operation.
The birthplaces of Alex, Ben and Cindy are India, Vietnam and China, in some order. Alex has never been to India. Cindy was not born in China, and her birthplace is not India. Find each person’s birthplace. Enter Alex; Ben; Cindy, using country names in that order.
For this puzzle, the three birthplaces are different; “home country” refers to birthplace, and “never been to India” excludes being born there.
Joanna goes to sleep at 11 p.m. and wakes at 6 a.m. the next day. She keeps this routine for 4 weeks. How many hours does she sleep altogether? Count 28 nights.
The police arrested four suspects who know one another. They know which one of them stole a wallet, but the police found the wallet on none of them. Sam: “I did not steal the wallet.” Ben: “Sam is lying.” Tim: “Ben stole the wallet.” Denny: “Ben is lying.” If exactly one of them tells the truth, who stole the wallet?
The diagram shows a cube with faces A, B and C labelled and a 3×3 grid with six squares labelled 1–6. Tip the cube so face C lies on square 1, then so face B lies on square 2, and continue along the numbered squares until square 6. What is the sum of the square numbers on which face B is on top?
The first three terms are 1,9,8. Each later term is the remainder when the sum of the preceding three terms is divided by 3. Thus the fourth term uses terms 1–3, the fifth uses terms 2–4, and so on. What is the 2019th term?
Daniel takes exactly 1 hour 17 minutes to travel to school. His lesson starts at 7:45 a.m. He wants to arrive 15 minutes before the lesson. When must he leave home? Enter a 24-hour time as HH:MM.
Jannah starts a movie club at school. In week 1 she recruits two members. From week 2 onward, each new member recruited in the preceding week recruits two new members. How many members are there after 3 weeks, including Jannah? All recruits are different people and nobody leaves.
On a meadow, there are six more birds than rabbits. The rabbits have six more legs altogether than the birds. How many birds and rabbits are there? Each bird has 2 legs and each rabbit 4. Enter birds; rabbits.
Twenty distinct points are given, with exactly three collinear points. How many triangles have vertices among these points? Interpret this as exactly one collinear triple and no other collinear triple.
