SASMO 2027 · Grades 4-5 · SET 004 · Self-study

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.

The figure is made from 20 equal-sized equilateral triangles. How many equilateral triangles of any size does it contain?



Enter a number or exact fraction only.

Peter has an old clock that loses 5 minutes every actual hour. For example, if set correctly at 9 a.m., it shows 9:55 a.m. when the actual time is 10 a.m. Every morning Peter resets it to the correct time at 7 a.m. before school. What time does it show immediately before each daily reset? Enter the hour in the morning as a number.



Enter a number or exact fraction only.

Elmo visits the park every Wednesday. If 1 January 2017 was Sunday and February had 28 days, what was the last date in March 2017 on which Elmo visited the park? Enter the day of the month only.



Enter a number or exact fraction only.

Calculate $C=\dfrac{\frac1{2018}+\frac1{2017}+\cdots+\frac12}{\frac{2017}{1}+\frac{2016}{2}+\cdots+\frac1{2017}}$. Enter an exact fraction.



Enter a number or exact fraction only.

Editorial note: calculate the fraction exactly as printed here. The source solution swaps its numerator and denominator; that discrepancy is explained after answering.

A semicircle with centre O overlaps parallelogram ABCD as shown. Its diameter AB is 12 cm. Find the total shaded area, in cm².



Enter a number or exact fraction only.

Fill all five blanks. Given 21 × 9 = 189, 321 × 9 = 2889, 4321 × 9 = 38889, find:
(a) 54321 × 9; (b) 654321 × 9; (c) 7654321 × 9; (d) 87654321 × 9; (e) 987654321 × 9.
Enter the five results in order, separated by commas, without spaces or digit-grouping separators.

Find the value of 218 + 19 + 111 + 505 + 212 + 35.

2 October 2017 was Monday. What day of the week was 1 September 2017? Enter the weekday in English or Vietnamese.

A truck has six wheels and a car has four wheels. Fourteen trucks and cars in a car park have 72 wheels altogether. How many trucks and how many cars are there? Enter trucks,cars, in that order, separated by a comma.

Four lamps form a 2 × 2 array. R, Y, B and W mean red, yellow, blue and white. Initially the top row is R Y and the bottom row B W. In minute 1 the two rows exchange colours; in minute 2 the two columns exchange colours. Repeat these two actions alternately, once per minute. What are the colours at minute 60? Options list top row / bottom row.

Alex visits the library every 4 days, Ben every 6 days and Zach every 8 days. They all visited together on Wednesday. On which weekday will they next visit together? Enter the weekday in English or Vietnamese.

The rectangle is made from six small squares, each with side 2 cm, arranged as shown. What is its perimeter?

A, B and C are the centres of three congruent circles. Each radius is 10 cm. Find the total shaded area, in cm², using π = 3.14.



Enter a number or exact fraction only.

Diagram convention: each centre lies on both other circles, so AB = BC = CA = 10 cm. Only the three pairwise-overlap lobes outside the central triple overlap are shaded. These relationships are implicit in the source drawing.

Find P in the sequence 41, 12, 82, 53, 24, 94, 65, 36, P. Enter P using two digits, including a leading zero if needed.



A finite list does not force a unique continuation. This is a pattern-recognition exercise asking for the source’s intended continuation; the intended rule is explained in the solution.

The figure is formed from congruent squares with side 4 cm. What is its perimeter, in cm?



Enter a number or exact fraction only.

In the multiplication shown, different letters represent different digits from 0 to 9. Find E. Printed numerals keep their usual fixed values.



Enter a number or exact fraction only.

Amy, Bob, Chris and Doris are each either a truth-teller, who always tells the truth, or a liar, who always lies. Amy says, “Exactly one of us is a liar.” Bob says, “Exactly two of us are liars.” Chris says, “Exactly three of us are liars.” Doris says, “All of us are liars.” At least one statement is true. Determine the type of each person. Enter four letters in the order Amy, Bob, Chris, Doris: T for truth-teller and L for liar, with commas.

In the multiplication SASMO × 4 = OGAMS, different letters represent different digits and each five-digit number has a nonzero first digit. Find SASMO.



Enter a number or exact fraction only.

The source states that 3 February 2019 is Saturday and that 2019 is not a leap year. Under that stated weekday assumption, what weekday is the last day of February? Enter the weekday in English or Vietnamese.



Calendar discrepancy: the stated weekday for 3 February 2019 is not the real-calendar weekday. Treat “3 February is Saturday” as a hypothetical premise for this exercise; do not replace it with the actual calendar.

A staircase has 10 steps. Starting on the ground, Peter climbs either 2 or 3 steps each time. In how many different ways can he reach exactly the 10th step? Different orders of moves count as different ways.



Enter a number or exact fraction only.