Call Your Grandmother

A grandmother has four grandchildren, Alain, Brain, Cain, and Daine. They all call her on January 1st and then Alain calls her every second day, Brain calls her every third day, Cain calls her every fifth day, and Daine wants to choose the rule, so that the granny has the smallest number of days without calls. ##What is the best strategy for her?



A good daughter phones her elderly mother every other day. A son of the same mother phones her every third day.

What is the fraction of days when she does not receive a call from the lovely children?


Who Solves Puzzles

Vladimir Arnold explained: “everybody who considers the thinking culture an essential part of the personality development.

This is an example of Vladimir’s puzzle:

“The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.

American school students had been coping successfully with this problem over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why?”

If you did not find the explanation check the answer.

May 1st Logic

Who does not belong?



Gerry says to Jane:

“Imagine that you have about one thousand dollars cash in your wallet,

which we round to the exact number of 1024,  and you enter a restaurant.

What do you choose as a starter?”

Which is Gerry’s most likely profession?


Funniest Aplusclick Puzzles

Math is Fun!

How many people left their footprints on the rocks?


What Is The Chance To Obtain $1,000,000?

Austin and Betty are entrepreneurs with many ideas. They need initial investment. A venture capitalist Craig decides to invest one million dollars  in a new business.  One at a time, Austin and Betty ask Craig for the initial investment in a new business.

Austin starts first and he has 25% chance to convince Craig in an attempt. Austin and Betty have equal chances to get $1,000,000 at the end.

What is Betty’s probability to get $1,000,000 in a single attempt?


What Makes Us Successful

Grit: The power of passion and perseverance

The Best Aplusclick Puzzle 2020

Here they go


Brainaire or Billionaire

Being a brainaire makes you feel probably better than just being a billionaire, isn’t it?

You can earn billions brain coins at Brainaire website that is full of logic brainteasers and funny questions. It is free and everything depends on your intelligence and your persistence. Give it a try at . You will not regret.

This is a sample question for a Brainiare:

What is the largest of the four options?



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?