The Best Aplusclick Puzzle 2020

Here they go


Understanding Pandemic Statistics

Real examples help to better understand how to interpret the statistics.

False Positive Paradox: A particular medical test for a disease is 96% accurate. If one has the disease, the test comes back ‘Yes’ 96% of the time, and if one does not have the disease, the test comes back ‘Yes’ 4% of the time.

If  100  of 10000 tested patients have the disease, what is the probability that the person with the diagnosis ‘Yes’ has the disease?



Effective Average Infection Ratio: R is the effective average infection ratio for a disease, also known as the reproduction number. It is the average number of secondary infections caused by one person. (Infections caused by the secondary infections – which would be tertiary infections – are not counted). Consider 50 infected people. Suppose 49 spread the infection to nobody, but one person spreads the infection to 60 people.

What is the R-value?



Leslie Green asks: How would you propose to deal with the COVID-19 pandemic, given information current at the time of writing (11 October 2020). 

A. Severe lockdown for 4 weeks

B. Ignore it and carry on as normal

C. Partial lockdown and wait for a vaccine

D. Some other idea



The Pfizer COVID-19 vaccine-candidate interim results from 8 Nov 2020 showed 38,955 participants in a placebo controlled double-blind trial.
94 participants  became “evaluable”, which we presume to mean they showed COVID-19 symptoms. The analysis presented was that the vaccine efficacy rate was above 90%. What is the maximum number of (genuinely) vaccinated people who showed COVID-19 symptoms?


Variability Analysis on COVID-19 Interim Trial Data by Leslie Green


Is there any rational justification for being wary of vaccines?



In the UK, December 2020, up to 2 million university students were potentially going home for Xmas during the middle of the COVID-19 pandemic. A new fast COVID-19 test had been developed to spot the causative virus, SARS-CoV-2. These lateral flow tests had the characteristics shown in the image. At the time, around 1% of the population had the virus within the community.

The scientific advice, given on prime-time news channels, was that a pair of negative tests meant it was safe to go home, as a negative test meant a 99.75% chance of not having the virus.

Was this true, and good advice?



Two or Three

z10266There are 5 counters in a bag. Three are Argentinean (blue) and two are Brazilian (green). Three counters are randomly picked out of the bag, one by one. They are not returned to the bag.



What probability is higher?

A. The probability of choosing three Argentinean counters in a row.

B. The probability of choosing two Brazilian counters in a row and then one Argentinean counter.

Find the answer.

Secret Agent 007

Seven secret agents are on payroll of a government.

Secret agent 001 spies on a secret agent who spies on secret agent 002,

who spies on a secret agent who spies on secret agent 003,

who spies on . . . spies on secret agent 007

who spies on a secret agent who spies on secret agent 001.  

Who spies on secret agent 007?




Aplusclick Best Puzzles 2019

These are the Best Puzzles published at in 2019.









Back to School – Friendship Math

Group Of Children Sitting On Bench In Mall

It is the first day of a new school year, and this class has only 10 students.  Ashley has 9 friends, Betty has 8, Caleb has 7, Derek has 6, Elaine has 5, Graham has 4, Henri has 3, Ivana has 2, Julie has 1.  Name one of Fred’s friends.


friends4In a group of 4 school children, each child has exactly two friends, just one of which is their best friend. What is the minimum possible number of children for whom their best friend is also that friend’s best friend?



It is the first day of a new school year, and this class has only 10 students.  Ashley has 9 friends, Betty has 8, Caleb has 7, Derek has 6, Elaine has 5, Graham has 4, Henri has 3, Ivana has 2, Julie has 1.  How many friends does Fred have?


It is the first day of a new school year, and this class has only 5 students. Amy has no friends yet. Betty has one friend. Chris has three friends. Derek has two friends.  How many friends does Ellie have?


In a group of five students, Ann has one real friend among them, Betty has two,  Craig has three, and Dianna has two. How many real friends does Edgar have in the group?


Motorway Problem

How to choose the shortest road that connects several towns. This is a story about local and global minimums. Excellent presentation  of soapy films.

18 Best Aplusclick Puzzles of 2018

New challenges:

What is the easiest way to make it correct?            Answer


In what Olympic sport does the winner cross the line facing backwards?      Answer


What time is it?         Answer


What is the necessary mirror size?     Answer


Find all 18 best puzzles at

Singapore Math


Singapore math  is a teaching method based on the national mathematics curriculum used for kindergarten through sixth grade in Singapore. Singapore math, also known as the “mastery approach”: students learn a specific concept  in a linear progression before moving to the next more complex subject. Students learn and master fewer mathematical concepts at greater detail using a three-step learning process: concrete, pictorial, and abstract. These are techniques of the teaching methods: to cover fewer topics in greater depth, handling objects such as pencils, dice, or paper clips, pictorial visualisation by drawing diagrams, bar modelling (a pictorial method used to solve arithmetic problems). Bar modelling is far more efficient than the “guess-and-check” approach. A 2015 study of 140 schools in the UK by found that the mastery approach improved the speed at which students learned math skills.

This is how Jeff Bezos, the richest man on the planet teaches maths to his children.



Math Symbols

We use math symbols to express complex mathematical texts in a shorter form.

=   replaces   “is equal to

+ replaces “and

×   replaces   “multiplied by

. . . .

There are many Greek symbols like   π ∑   and special symbols like   √ ∞ ∈   in mathematics.

John David Walters explains where math symbols come from in the video: