The Best Aplusclick Puzzle 2020
January 5, 2021 Leave a comment
Here they go

Math and Logic Puzzles
February 16, 2020 Leave a comment
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?
November 9, 2016 1 Comment
Math and Logic are full of paradoxes.
1. Achilles and the Tortoise The Paradox of Achilles and the Tortoise was described by the Greek philosopher Zeno of Elea in the 5th century BC. The great hero Achilles challenges a tortoise to a footrace. He agrees to give the tortoise a head start of 100m. When the race begins, Achilles starts running, so that by the time he has reached the 100m mark, the tortoise has only walked 10m. But by the time Achilles has reached the 110m mark, the tortoise has walked another 1m. By the time he has reached the 111m mark, the tortoise has walked another 0.1m, then 0.01m, then 0.001m, and so on. The tortoise always moves forwards while Achilles always plays catch up. Why is Achilles always behind the tortoise?
2. Bermuda Triangle Paradox. Why the sum of the interior angles of the Bermuda triangle is not 180 degrees?
3. Simpson Paradox. The average score for dance of boys and girls in class A are 16 and 21, respectively. The average score of boys and girls in class B are 15 and 20, respectively. Twenty percent of class A students are girls. Forty percent of class B students are girls. Which class has a higher average score?
4. Braess paradox. The diagram shows a road network. All cars drive in one direction from A to F. The numbers represent the maximum flow rate in vehicles per hour. Engineers want to construct a new road with a flow rate of 100 vehicles per hour. Drivers randomly choose the road at crossroads. What new road decreases the capacity of the network (the number of vehicles at point F)?
5. Barber Paradox In a city, the barber is the ‘one who shaves all those, and those only, who do not shave themselves.’
Who shaves the barber?
6. The Two Envelope Paradox. One envelope has twice as much money as the second one. Gerry does not know which envelope contains the larger amount. He takes one of the envelopes, counts the money, and is offered the chance to switch the envelope. He thinks “If the amount of money in the chosen envelope is X dollars, then the other envelope contains either 2X of 0.5X dollars, with equal probability of 0.5. The expected value of switching is 0.5 (2X) + 0.5 (0.5X) = 1.25X. This is greater than the value in the initially chosen envelope. It is better to switch.” What is your advice?
7. Potato Paradox. I have 100kg of potatoes, which are 99 percent water. I dry them until they are 98 percent water. How much do they weigh now?
8. Leonard Euler’s Paradox. Why the average of all of the numbers is not a zero?
1, -1, 2, -2, 3, -3, . . .
9. Friendship Paradox. Your friends have more friends than you. Why?
10. Uninteresting Number Paradox. How many uninteresting numbers exist?
11. Gabriel’ Horn Paradox. The shape obtained from rotating the equation about x-axis resembles a trumpet. If we need an infinite volume of paint to paint the infinite horn, how much paint does the horn can contain inside itself?
12. Pop Quiz Paradox. A teacher announces that there will be a quiz one day during the next week. The teacher gives the definition that they would not when they come in to the class that the quiz was going to be given that day. The brightest student says that the quiz cannot be on Friday because they will know the day. With the same technique, she eliminates Thursday, Wednesday, Tuesday, and Monday. “You cannot give us a pop quiz next week” she says. When does the teacher give the pop quiz? I know the paradox from Charles Carter Wald. Probably, Martin Gardner described it for the first time in The Colossal Book of Mathematics.
10. Uninteresting Number Paradox
December 13, 2015 2 Comments
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 strategies 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
The 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?
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?
Gambling is bad for your health and budget!
May 11, 2014 Leave a comment
“In 1932 Malba Tahan published what would became one of the most successful books ever written in Brazil – O Homem que Calculava – The Man Who Counted.”