## 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 www.aplusclick.org/brain/ . You will not regret.

This is a sample question for a Brainiare:

What is the largest of the four options?

M L XL X

## JUICE, SODA, and LUCKY

A drinks dispenser has three labelled buttons: JUICE, SODA, and LUCKY. If you press LUCKY you are supposed to get either juice or soda with equal probability.

Each button is wired to exactly one of these functions, but each function is not necessarily wired to exactly one button.

Assuming that you are clever, but unlucky, how many button presses are required to establish exactly which button does which function?

## Big Ben Maths

Big Ben is the nickname for the Great Bell of the clock at the north end of the Palace of Westminster in London, United Kingdom.

A pile of old coins helps to keep the clock mechanism accurate.  The pennies are stacked on the pendulum of the clock and have acted as weights. Adding or taking away coins effects the pendulum’s centre of mass and the rate at which it swings. A single penny will change the clock’s speed by two fifths of one second per day.

How does the weekly time change if we add 5 pennies to the pendulum?

At twelve o’clock, twelve chimes  ring from the great bell in 44 seconds. ## How long does it takes to ring the hours at 15:00 ?

## Pythagorean Triples Were Known 1,000 Years Before Pythagoras

The Babylonian clay tablet from the collection of Columbia University dating from 1,000 years before Pythagoras’s theorem is a trigonometric table which has 15 pairs of numbers forming Pythagorean triples: three whole numbers a, b and c:

a2 + b2 = c2

The tabet is known as the world’s oldest trig table. Babylonians used the base-60 numbers, which permitted many more accurate fractions than the contemporary base 10. For example, 2/3 = 0.6666… (or 40 minutes) was a finite number. The base-60 system were inspired from such shapes as a circle and the regular hexagon (see an example).

## Car Owner’s Puzzles

Can a specific subject provokes interest to Math?

For example, cars. How much does the gas cost in a month? What speed to choose? When do I need to change the tires? How to be on time? How much do I pay for a car during its life? . . .

What are other intersting subjects? Finance? Love? Sport?

## Fermi Problem

Often, a problem solver might estimate the required value without very much information. He/she might aim to get an order of magnitude estimate. The estimation technique is named after physicist Enrico Fermi, as he was known for his ability to make good approximate calculations with little or no actual data. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds.

The classic Fermi problem, generally attributed to Fermi, is “How many piano tuners are there in Chicago?” – Wikipedia

Several simple examples of Aplusclick Fermi problems:

Tennis Balls in a Bus

English Language Words

Demographics

Security Control

## Dream Math

Everybody dreams.

The boy dreams of being an astronaut.

How long does he need to study and work until his dream can become reality?

Which job does not require math?

The photograph courtesy of Roland Sauter

## Estimate or Calculate?

” in the real world, we constantly settle for estimates, whereas mathematics — see the SAT — demands that you get the answer precisely right.” – Andrew Hacker in The New York Times article “The Wrong Way We Teach Math

Estimate or Calculate?

My answer is one of them and do it fast.

## Coin Landing On Its Edge

I flip a fair Swiss franc* and it falls in mousse**. What is the probability that the coin stays on its edge after the mousse melts?

*One Swiss franc is about 1 USD; diameter 23.20mm , thickness 1.55mm, weight 4.4g.  During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge several times.
**A mousse (French ‘foam’) is a prepared food that incorporates air bubbles to give it a light and airy texture.

Solution

The probability  that the coin stays on its edge is about 4% for a Swiss franc and 5% for an American dime.

http://www.aplusclick.com/t.htm?q=5135

Such an outcome on a hard and flat surface is fairly unlikely, having been estimated at approximately 1 in 6000 tosses.

https://en.wikipedia.org/wiki/Coin_flipping