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.
Continue the illustrated diamond pattern. How many black diamonds are in Figure 6?
Original labels: Hình 1, Hình 2, Hình 3 mean Figure 1, Figure 2, Figure 3.
Seven points are marked: six lie on a semicircular arc, including the two endpoints of its diameter, and the seventh is the centre. How many triangles have all three vertices among these points?
Fill the grid with four shapes (circle, triangle, square, pentagon) and numbers 1,2,3,4 so that every row and every column contains each shape once and each number once. What shape belongs at the question mark? Enter the shape name.
Answer only the shape; the number is not requested. Shapes and numbers each obey their own no-repeat rule.
Alex plays soccer every third day, Ben every sixth day, and Zach every eighth day. They all played together on Wednesday. On what day of the week will they next play together?
Find the shaded area in the diagram. The large square has side length 20 cm. Use π=3.14. Give the area in square centimetres.
Interpret the curves as the quarter-circles indicated by the source construction: one has radius 20 cm and the two smaller ones have radius 10 cm; the internal lines bisect the square.
Insert +, −, × or ÷ into 2 □ 3 □ 4 □ 5. Operations may repeat, and brackets may be inserted. Keep the digits in this order. What is the largest two-digit whole number obtainable?
Mandy uses all four cards 1,4,3,2 once each to form four-digit numbers. If 3 is always in the tens place, how many different numbers can she form? For example, 1432 is allowed.
Use the digits 1,2,3,4,5,6 exactly once to form $\overline{abcdef}$. The full number is divisible by 6; $\overline{abcde}$ by 5; $\overline{abcd}$ by 4; $\overline{abc}$ by 3; and $\overline{ab}$ by 2. Find every possible six-digit number. Enter them in increasing order, separated by a comma.
There may be more than one valid number; give all of them rather than choosing just one.
A blueberry cake was half eaten during the afternoon. Their mother asks three children. Ron says, “Harry ate the cake.” Harry says, “Ron lied.” Tony says, “I did not eat the cake.” Exactly one child tells the truth. Who ate the cake? Enter the name.
Puzzle interpretation: exactly one of Ron, Harry and Tony ate the missing portion; Harry is denying Ron’s statement about this cake.
Different letters A,B,C,D represent different digits from 0 to 9. The multiplication shown is $\overline{ABA}\times\overline{CD}=\overline{CDCD}$. Find A+B. Leading digits A and C are non-zero.
