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 jewel was stolen at an exhibition. Four suspects say:
David: “Ellen stole it.”
Ellen: “Fred did.”
Fred: “I have an alibi.”
George: “Do not believe what Ellen said.”
Exactly one suspect tells the truth. Who is the thief? Enter the name.
Puzzle interpretation: exactly one of the four stole the jewel. Fred’s alibi statement means “I did not steal it”, and George denies Ellen’s statement about this theft.
Twenty-five trees are planted at equal distances along a straight road. The distance from the first to the eighth tree is 56 m. What is the distance from the first to the last tree, in metres?
How many four-digit numbers satisfy each condition? (a) All digits are distinct. (b) All digits are distinct and at least one is odd. Use digits 0–9; a four-digit number cannot begin with 0. Enter answers (a),(b) in that order, separated by a comma.
Ben writes all integers from 1 to 100 on a whiteboard, then erases every digit 3. How many digits remain? Erase just each 3, not the whole number containing it.
Tom uses 1 cm-long matchsticks to make the house outline shown. The top uses 10 sticks, each vertical wall 8, each sloping side 2, and the base 12. What is the perimeter, in centimetres?
The four-digit number $\overline{5x1y}$ has four distinct digits. Find all digit pairs (x,y) such that it is divisible by both 2 and 3, and has remainder 2 when divided by 5. Enter the pairs in increasing x order as x,y; x,y.
