Everyday Brain Training

Millions people do everyday physical training / exercises. They want to keep their body in good shape.

Group of kids getting ready to raceWhy a smaller number of people intentionally do everyday brain training / exercises?

  • The absence of intelligence is not so visible as defaults of the physical shape.
  • Everybody thinks that he / she is enough smart.
  • Playing computer games is considered as a mental work.
  • No time, there are other priorities.
  • Lack of motivation / self-discipline.
  • There are not interesting intelectual challenges to meet everyday.
  •  . . .

Many types of work, games, discussions concentrate on a limited types of challenges. You can play many hours everyday, but the types of exercises are limited: just kill / catch somebody, and you do it again and again.

Aplusclick tries to respond to the challenges by creating a collection of different logic puzzles for all ages. There are several thousands different types of problems. Enough to do everyday training for many months.  Many of them demands exceptional intelligence.

Do your everyday 5-minute brain training at the free website Aplusclick and keep your brain sharp.

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Classics of Recreational Math

The classical recreational math authors are Lewis Carroll,  Henry DudleyMartin GardnerSam Loyd, and Yakov Perelman.

This an example of classical math puzzles: http://www.aplusclick.com/k/5423.htm :

(102 + 112 + 122) – (132 + 142) = ?

The picture “Mental Count” of Russian painter Nikolay Bogdanov-Belsky contains the simple calculation. Image source : Wikipedia



Logical Reasoning in Pattern Recognition

Bongard problem is a kind of puzzle invented by the Soviet computer scientist Michael Bongard (1924–1971) in the mid-1960s. He died in 1971 during a hiking expedition in the Pamir Mountains. The tests played an important role in the disciplines of cognitive psychology and cognitive science. Human logical reasoning has a great advantage over computer intelligence.

Be smart.   Train your brain!

Here several problems similar to the original Bongard problems go:

What is the main difference between the pictures on the left page and on the right page?

A. z5461

B. z5462

C. z5468

Try to solve the problem yourself before looking for the answers  in the A+Click Brainteaser Problems.



Harry Foundalis collected hundreds of Bongard problems.


The logic puzzle almost everyone gets wrong

This is a very famous logic problem:

“Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

  • A: Yes
  • B: No
  • C: Cannot be determined”


According to the Keith E. Stanovich in Scientific American more than 80 percent of people choose C, which is not the correct answer. The correct answer is A. Why?

This is another example of a similar problem:

There are only two handshakes in a meeting: John shakes hands with a person, this person shakes hands with Anna. Does a man shake hands with a woman in the meeting?


How to Solve a Problem – Read the Question

Try to solve the following problem suggested by Leslie Green:


What is the difference between the number of letters in UPPER CASE and lower case in the text?

Most of the people and me too answered the question fast: None.

If you give the same answer, read the question again.

The trivial advice is often useful: “Try to answer exactly to the question.”

Do you get another answer? What is it?

1932Another example:  A shopkeeper of a Dairy stands six feet tall and wears size 13 sneakers. What does he weigh?



Betting Math

Leslie Green’s Casino Problem

A bunch of Physicists, fresh from College, go to their local casino with plans to profit with their advanced gaming strategiesCasino Roulette - 3d render for Roulette. They have chosen a Roulette game where there are 36 numbers from 1 to 36, alternately colored black and red. There is only one green slot, which is usual in Europe but unusual in the USA. When the ball lands in the green slot, 0, all bets are lost to the House.

All participants place 223 bets. Each bet pays out at 1/1 odds, meaning you get your bet back plus an equal amount of winnings.

John bets only on RED, and only immediately after a run of 3 reds.

Sally bets only on EVEN, but only after the sequence ODD, ODD, EVEN, ODD.

Peter looks for a run of 8 events, either all ODD, all EVEN, all RED or all BLACK. He then bets against this run continuing.

At the end of the 223 bets, who is the most likely to have won?

Leslie Green’s Sports Betting Problem

736The all-male under-10 football team, the Hunky Heroes, are playing the all-girl under-12 football team, the Girly Girls. I am facilitating the betting, although this may not be strictly legal in all jurisdictions.

Buddy and his friends have put a total of $200 on the favorites, the Hunky Heroes, to win. If they win I have to pay out a total of $3 for every $2 placed.

Samantha and her friends have put a total of $50 on the Girly Girls to win. If they win I will pay out a total of $6 for each dollar placed. (Some people would call this 5/1 odds, where you win $5 for each dollar placed AND you get your $1 bet back).

Some of the parents have individually placed a total of $100 on a draw. In this case I pay out a total of $3 for each dollar placed.

Who has the greatest chance of winning?

Casino Statistics

In a casino on a Sunday,  90% of the visitors lost $200 each, # 9% of the visitors lost $1,000 each, and # the rest won $10,000 each. # If the profit of the casino is $340,000, how many people visited the casino?

The answer

Bankrupt Business

Jane and Gerry visit a casino. In one game, they have a 1/5 probability of winning $100 and 1/2 probability of losing $50. They have also a chance of no win / no loss. What is the most likely amount of money they will win (or lose) at the end of 100 games?

The answer

Gambling is bad for your health and budget!

Everyday Geek Questions

What happens once in a minute, twice in a week and once in a year?


I will be X years old in year X2. How old am I?


How many planes of symmetry does a cube have?


“1” costs $10. “20” costs $20. How much does “100” cost?