SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
In mathematics, $a^2=a\times a$, $a^3=a\times a\times a$, $a^4=a\times a\times a\times a$, and so on. Find the difference between $2^5$ and $3^3$.
Shawn lives on the 6th floor of an apartment block. Jessie lives on the 3rd floor of the same block. Shawn takes 4 minutes to walk from the 1st floor to Jessie’s apartment. How many minutes does he take to walk from the 1st floor to his own apartment?
Assume each floor-to-floor climb takes the same time, with no stops.
The teacher has fewer than 30 sweets. If she gives each child 3 sweets, 4 sweets remain. If she gives each child 4 sweets, she is short of 3 sweets. How many sweets does she have?
There are 5 green, 4 white, 3 red and 2 orange balls in a bag. Shawn is blindfolded and selects balls. What is the least number he must select to ensure that he has 3 balls of the same colour?
Select without putting any balls back into the bag.
There were 14 children at a Chinese New Year party. Each girl received 4 balloons and each boy received 2 balloons. Altogether 44 balloons were given out. How many girls were at the party?
During the COVID-19 lockdown, three girls were suspected of travelling overseas. An investigator from the Ministry of Health interviewed them.
Raina: “I was at home all day every day.”
Sofia: “I went to the Great Wall of China.”
Tania: “Raina posted an Instagram photo of herself at the airport!”
If one girl was lying, who should be quarantined?
This is a fictional logic puzzle. The source does not specify photo dates, the home country or quarantine rules. Explain any assumptions and whether the conclusion is certain; this response is marked manually.
$\overline{ab}$ is a two-digit number. Appending the digit 1 gives $\overline{ab1}$; putting 1 in front gives $\overline{1ab}$. Their difference is 414. Which digit does $b$ represent?
A bag contains 9 white, 5 red and 3 black balls. What is the minimum number Shawn must draw without replacement to ensure at least one black ball? He cannot look into the bag.
