SASMO 2021 Grade 4

Platform: start at 0; Q1–15 are worth 2 each, Q16–25 worth 4 each; wrong/blank 0; maximum 70. Official SASMO reference: initial 15, Section A +2/−1/0 (correct/wrong/blank), Section B +4/0/0; maximum 85.

Calculate $654+546+465-456-564-645$.

How many two-digit multiples of 3 can be formed using the digits 1, 3, 5 or 9? For each number, each digit can only be used once.

Toby wrote down all the numbers from 100 to 200 on the whiteboard. Which digit appeared the greatest number of times?

How many ways are there from point A to point B if you can only move to the right or down?



Move only along the drawn lines; do not add missing grid segments.

Jessie takes 12 minutes to go from the 1st floor to the 3rd floor. How long would it take her to get from the 3rd floor to the 10th floor?

Assume every floor-to-floor interval takes the same time, with no extra stops.

If the five-digit number 3625A is divisible by 9, what is the value of the digit A?

A regular octagon is an 8-sided figure with all angles equal and all sides equal. Six regular octagons are arranged as shown. If the perimeter of the whole shape is 570 cm, what is the perimeter of each octagon?



The six octagons are identical and joined along the full sides shown.

Which figure is a rotation of the figure on the right?





Rotate the whole solid without moving or recolouring individual cubes; preserve the black-cube pattern.

David chooses four numbers from the table so that he picks exactly one number in each row and exactly one in each column. What is the greatest possible sum?

Which figure cannot be drawn without lifting the pen and without tracing the same line more than once?



Treat each drawn crossing as a junction and every drawn segment as an edge to be traced exactly once.

Fred always tells the truth on Tuesdays, Wednesdays and Thursdays, always lies on Sundays, and may tell the truth or lie on the other days. On five consecutive days, he was asked his grade. His answers, in order, were Primary 3, Primary 4, Primary 5, Primary 3 and Primary 2. Which grade was Fred in?

Fred’s grade stays the same throughout these five days.

Which of the following is the sum of five consecutive whole numbers?

Running at the same rate, 10 identical printers can print 10 pages in 10 seconds. At this rate, how many printers are needed to print 60 pages in 1 minute?

All printers work continuously at the stated constant rate, with no setup delay.

Alison is 30 years older than Bernard. Last year, Bernard was 20 years older than Caitlyn. Next year, Caitlyn will be 10 years older than Donald. Their total age five years ago was 180 years. How old is Donald now?

Melissa, Noah, Olivia, Pierre, Qiqi, Rain and Susan answered 2, 4, 6, 8, 10, 12 or 14 questions correctly in SASMO 2020, not necessarily in that order. Noah answered 6 more correctly than Susan. Rain’s number was 4 times Olivia’s. Melissa and Qiqi together answered 6 times as many correctly as Pierre. How many questions did Susan answer correctly?

The seven listed counts are used exactly once each.

How many triangles are there in the figure?



Count all triangles, including larger composite ones. Treat intended straight lines and shared intersections as exact despite scan thickness.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

Nine students stand in a line to receive SASMO awards. Seven are Primary 5 students, five are gold award winners, and four are silver award winners.

- The two neighbours of every silver awardee are gold award winners.
- No two gold awardees stand next to each other.
- The first and last students are not Primary 5 students.

How many of the nine students are not Primary 5 gold awardees?

Each student has exactly one of the two awards. A silver winner must have a neighbour on both sides.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

The solid shown was painted on all six faces and then cut into 54 smaller cubes. How many of these cubes have at least two faces painted?



Source clarification before answering: the dark scan does not show subdivision lines clearly. Use the source solution’s intended rectangular block of 3 × 3 × 6 equal cubes (six 3 × 3 layers). Only the exterior is painted before cutting.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

The sum of the digits of 2021 is 5, and 2021 is one more than a multiple of 5. What is the next number after 2021 with both properties?

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.

The bar graph shows how many seashells Shelly, Sharon, Sheila and Sherilyn had at first. All horizontal lines are equally spaced.

On day 1, Shelly gave half her seashells to Sharon. On day 2, Sharon gave 16 seashells to Sheila. On day 3, Sheila gave half of her total seashells to Shelly. On day 4, Shelly gave some seashells to Sherilyn.

After day 4, all four girls had the same number. How many seashells did Shelly give to Sherilyn?



The bottom horizontal line represents zero; no seashells are lost or added except the stated transfers.

Input: enter a whole number without units; leading zeroes from the paper answer grid may be omitted.