Find three fastest horses

 Q We have 25 horses we need to find fastest 3 horses.We can race 5 horses together. How many minimum races we require?

We have 25 horses and can race only five. Let’s Divide horses in groups of five horses each. Now we have five groups and each group has five horses.

Next, let us name our groups as A, B, C, D, E with horses 

• A1,A2,A3,A4,A5
• B1, B2, B3,B4, B5
• C1, C2,C3,C4,C5
• D1, D2, D3, D4, D5
• E1,E2,E3, E4, E5

Next, let us suppose we have following winners from the 5 races of above groups.

• A1, A2, A3
• B1, B2,B3
• C1,C2,C3
• D1,D2,D3
• E1,E2,E3

Next, we will have a 6th race of all the winners, and we will have a fastest horse among all. So now we have the horse at first position which is A1.Let the outcome of the 6th race be as follows.

• A1,B1,C1

Since B1 lost to A1, also A2 lost to A1 so we need to have a race between 2 to find third fastest horse. Also for the 3rd fastest horse we have choices B2, A3, C1, A2,B1 since C1 , A3, B2 came in second and third positions have a race among these horse’s to find the second and third fastest horse. This will be our seventh and final race.

So we require 7 races in total.

Cut the circular cake in 8 in 3 cuts

1. Make 2 cuts vertical and horizontal and cut 3rd one from center along complete area so we have 4 pieces dived by 2 i.e. 8 but this will be unfair as half the pieces will not have cream so let's find 2nd way out

2. Make 2 cuts vertical and horizontal now stack the 4 pieces 1 on each other and cut along again you will have 8 pieces in all.

Weight the flight

A flight started from chennai airport to thiruvananthapuram for a journey of around 2 and half hours..The weight of the flight in chennai airport is 1000kg, what would be the weight of the flight in thiruvananthapuram airport?

 Ans: Weight would be less because amount of fuel is reduced.

Lowest weighed ball

Q1. There are total of 10 balls , out of that 9 were of same weight and 1 is off diff weight, find that ball using minimum measurement?

Ans:
Divide balls into group of 3,3,3,1

Weight the first 2 groups of 3 balls if they are equal then they don't have the ball the group with lowest weight has the ball

Now we have 4 ball's left weigh them by dividing them into 2 groups of 2 balls. The group with lowest weight has the ball

Now weigh 2 ball's with each other and you will have ball with lowest weight.

Complementary function and Particular Integral

Complementary function (or complementary solution) is the general solution to a differential equation dy/dx + 3y = 0.

Particular integral (I prefer "particular solution") is any solution you can find to the whole equation.

The general solution of a differential equation, involving an arbitrary constant, represents more than one, even infinitely many, solutions.

The solutions obtained by assigning definite value to the constant is called a particular solution. typically, the value is determined by making the solution satisfy a given condition, traditionally referred to as initial condition.

What is Probability and It's types

Probability theory mathematically formulates incomplete knowledge pertaining to the likelihood of an occurrence. For example, a meteorologist might say there is a 60% chance that it will rain tomorrow. This means that in 6 of every 10 times when the world is in the current state, it will rain.


Probability can of 3 types counting,geometry and algebra


Probability of counting

Let P(event) be
the probability of some event occurring. We can often determine P(event) by counting the number
of successful outcomes and then dividing by the total number of equally likely outcome


Probability as a geometry

Sometimes it is impossible to count the total number of events because there are infinitely many
possibilities. Some problems involve evaluating points on a line segment or in space, or particular
values of a continuous variable such as time.

Probability as Algebra

Here we view probabilities as variables. We then apply algebraic methods to find the values of those variables.

Source: http://www.artofproblemsolving.com/Resources/Files/probarticle.pdf

We will discuss some questions on these 3 on next posts

Sales by Product



Sales by Location of Company(multiply each value by 10 so sales at paulo is 550 millions and so on)





Now I have a question
Q If 20% of Domestic footwear were from Paulo.What was the value of the sales of other products in paulo?