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?



Online Shopper Decision

You are buying a roller on Amazon. Four similar rollers have the same functions, the rollersame price, the same look, but different ratings.

Which product do you choose?

A. 8 positive ratings (8 total ratings)

B. 45 positive ratings (48 total ratings)

C. 90 positive ratings (98 total ratings)

D. 177 positive ratings (198 total ratings)

Find the answer at


Chance for a Would-be Bride

girl-straws There was a tradition in old Russia. A would-be bride gathers six long pieces of straw and grasp them in her hand. She then randomly ties pairs of knots on the top and the bottom. Since there are six blades of grass sticking out above and below the hand, she will tie three knots on the top and three knots on the bottom. If she forms one big ring, she gets married soon.

Estimate the probability that the girl will get married soon.

The problem is mentioned in The New York Times NUMBERPLAY and it is credited to Sunil Singh.


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.

Unrepresentative Voting

Leslie Green explains how our voting systems can be unrepresentative.


Five different parties are standing in an election for one representative. The voting  methods:  First past the post (FPTP): the party with the highest vote-count wins.

Is the voting system representative?

The no-pets party has 30% of the total, whereas parties that want pets are the remaining 70%.  As it stands the FPTP system would vote-in the no-pets party, which does not represent the view of the electorate.  What has happened is that the pro-pet movement has splintered, dividing the vote. In order to overcome this, one can use a transferable vote scheme so people can vote for their preferred option safely, preventing the hated no-pets party from winning.

A more detailed analysis can be found in an example.

First Woman to Win the Abel Prize

Karen Uhlenbeck to win the most prestigious award in mathematics – the Abel Prize.


The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA.

Her theories have revolutionized our understanding of minimal surfaces, such as those formed by soap bubbles.

Niels Henrik Abel (1802–1829) was a Norwegian mathematician. In spite of his short life, he made significant contributions to a variety of mathematical fields.