Math Homework Help

You write down the following 8 digit number on a piece of paper
1 2 3 4 5 6 7 9
Then ask your friend to circle one of the digits. Say 5

You then ask your friend to multiply the 8 digit number by 45, and magically the result ends up being:

1 2 3 4 5 6 7 9
x 4 5
—————
5 5 5 5 5 5 5 5

with the answer as a raw of the chosen number 5

The Secret!!!

When your friend circles a number, you need to multiply the chosen number by 9 in your head. Then you need to ask your friend to multiply the 8 digit number by the number you have worked out and you magically get the answer as a raw of the chosen number.

John was born in 19ab. The two digit number ab when divided by 2 gives his age on his birthday in 1999. Can you tell me how old was he?

Solution
33 years

Today I have a very simple puzzle for you.

It is a small town railway station and there are 20 stations on that line. At each part of the 2 stations the passengers can get tickets for any of the other 19 stations.

How many different kinds of tickets do you think the booking clerk has to keep?

Solution
The answer is simple. 19×20=380

Kathy and Jane were selling sweets in the market place. Kathy at 3 for a dollar and Jane at 2 for a dollar. One day both of them were obliged to return home when each had thirty sweets unsold. They put together the two lots of sweets and and handing them over to a friend, asked her to sell them at 5 for two dollars. According to their calculation, after all, 3 for 1 dollar and 2 for 1 dollar was exactly same as 5 for 2 dollars.

Now they were expecting to get 25 dollars for the sweets as they would have got, if sold separately. But much do their surprise they got only 24 dollars for the entire lot.

Now where did the 1 dollar go? Their friend was a cheat?

Solution
There isn’t really any mystery. While the two ways of selling are only identical, when the number of sweets sold at 3 for 1 dollar and 2 for 1 dollar is in proportion of 3:2. So , if Kathy had sold 36 sweets and Jane 24, they would have fetched 24 dollars (12 dollars each) , immaterial of, whatever sold separately or at 5 for 2 dollars. But if they had the same number of sweets which led to loss of 1 dollar when sold together, in every 60 sweets. So if they had 60 each (120 altogether) , there would be a loss of 2 dollars and so on.

In the case of 60, the missing 1 dollar arises from the fact that Kathy gains 2 dollars and Jane losses 3 dollars(If they share $12 each).

Kathy receives $9.5 and Jane $14.5, so that each loses $.50 in the transaction.

Today let’s relax a bit.

A peasant is convicted. He gets the death penalty. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If the peasant lies, he will be hanged, if he speaks the truth he will be beheaded. The peasant speaks a last sentence and to everybody surprise some minutes later he is set free because the judge cannot determine his penalty.

What did the peasant said?

The peasant said: “I shall be hanged!”

If the peasant was lying, he would be hanged. But that’s what the peasant was saying. So he speaks the truth. But if he speaks the truth, he would be beheaded, so then he was not speaking the truth. So it is impossible for the judge to determine whether the peasant speaks the truth or not. So therefore the judge cannot determine the penalty and sets the peasant free.

Don’t go away……. I need your help…….

My 2 year old son put a coin in an empty bottle and insert a cork into the neck of the bottle.
The bottle has a very nice shape. So I don’t want to break it.
How could I remove the coin without taking the cork out ?

Answer

Don’t worry for a solution. He himself found a way and took it out. He pulled the cork into the bottle and the coin came out.

1. Think of a 3 digit number where all the digits are different.
2. Reverse the digits
3. Subtract the smaller number from the larger number
4. Reverse the digits again
5. Add the numbers in steps 3 and 4

Whatever 3 digit number you choose the number will always be 1089!

Here is an example

1. 543
2. 345
3. 543 - 345 = 198
4. 891
5. 891 +198 =1089

Two trains start from two different stations A and B. One is going from station A to station B and another from station B to station A. If first train takes 8 hours to complete the journey and the second one takes 12 hours, when do the two trains cross each other?

Answer
The first and second train travel 1/8 and 1/12 respectively of the total distance of AB in one hour . So they cover 1/8 +1/12=5/24 of the distance AB in one hour. That means they will cross each other after 24/5 (4 hours 48 minutes) hours.

Yesterday I couldn’t write. Today I hoped to write about basic geometric concepts. But today also I am very busy and I haven’t enough time to write a long topic.

So we can have a small puzzle today. This is an ancient problem dating back to about 310 A.D.
Demochares had one-fourth of his life as a boy, one-fifth as a youth , one-third as a man, and has spent 13 years in his dotage. How old was Demochares?

Another problem of this kind:
A stone weights one Kilogram and half of its weight. What is the actual weight of the stone?

Solutions:
First Question
Let x be Demochares’s age.
Then, x/4+x/5+x/3+13=x
ie 47x/ 60+13=60
==>47x/60=47
==>x=60
So, Demochares was 60 years.

Second Question
2 kilogram

What is the peculiarity of 1729?

This number is known in the name of the famous mathematician Ramanujan.

Answer

This is the one and only one number which can be written as the sum of the cubes of two numbers in two different ways.

10^3 + 9^3 =1729
12^3 + 1^3 = 1729

Today again I have a puzzle. This one is not a typical math puzzle. You should use your common sense to answer this simple puzzle. Here we go……

Two identical trains, at the equator start travelling round the world in opposite directions. They start together, run at the same speed and are on different tracks.
Which train will wear out its wheel treads first?

You can post your answers in the comments section.

Update
The train travelling against the spin of the earth will wear its wheel more quickly, as the centrifugal force is less in this train.