GEOMETRY QUESTION

An equilateral triangle of side t, a square of side s and a circle of radius r touch each other in a right triangle ABC with vertical side BC=a. Find t in terms of a.

Source: Adapted from Sacred Mathematics by Fukagawa Hidetoshi and Tony Rothman (originally a Sangaku by Watanabe Kiichi)

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CREATE A 10 DIGIT NUMBER

Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.

FRACTION WITH ALL DIGITS

Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)? 

Example that doesn't work: 7192/38456 = 0.187

A PNC PROBLEM

Given 30 consecutive numbers, how many ways can you select 3 to get an even sum ?

AGE PROBLEM

Jack, John and Julie are talking about their ages.
"When you multiply mine and John's age you get a square number" says Jack.
"In 40 years, Jack will be as old as I am now", says Julie.
"In 10 years, our three  combined ages will be the same square number Jack was talking about" says John.
How old are Jack, John and Julie?

Source: Mathematical Puzzles and Problems [Kindle Edition] Daniel Benson (Author), FJ Bermann (Author), Alice Nielson (Illustrator)
Solution: Yes

Geometric problem

A circle is inscribed inside an equilateral triangle and an infinite set of circles are nested inside such that each circle touches the previous circle and the edges of the triangle act as tangents.

What fraction of the large red circle do the infinite set of smaller circles represent?
Lets see who gets this one...!!

FORM NUMBERS FROM 1,9,9,9

Today a new thing.. NOT A METHOD.. BUT A PROBLEM... Lets see who cracks it... The goal is to reach numbers from 1 to 100.. by using only 4 digits 1,9,9,9... 
U=You can use addition, subtraction, multiplication, division, power,root,factorial.. But you cant use square or cube.. u cant club numbers like 19 or 99...
so I wish to see at least comments for 50 numbers...
I will give two examples:
1=(9+9)/9-1 or (9-9)/9+1
2= root(9) -1 +(9-9)
Lets search for a genius mathematician here

VIDEOS FOR BETTER UNDERSTANDING

I have commented the videolinks for each of my posts.. as videos make one understand better.
Here also I provide the links:
1.https://www.youtube.com/watch?v=G1PIQzHXgak

2. https://www.youtube.com/watch?v=L3EbCNP9QJ0

3. https://www.youtube.com/watch?v=P3fYSO2ubkY

4. https://www.youtube.com/watch?v=ZWqfv7SKET4

Multiplying numbers in ONE LINE

A video can explain better than an image or a text.. So, here are 2 videos on IXI method of Vedic Multiplication,:
1. https://www.youtube.com/watch?v=VBh0BXgyrUk
2. https://www.youtube.com/watch?v=wZYiqAwasx0

DIVISION BY DHVAJANKA SUTRA

A new method of division for 2- digit divisors..A very good application of algebra to arithmetic.. lets see who cracks its logic

VEDIC DIVISIBILITY TESTS

Hi, this is a POST about VEDIC DIVISIBILITY TESTS by EKADHIKA METHOD:
Lets see if anyone can get its logic:

SQUARE ROOT BY DIVISION

Todays post about- Square root by division. But different from school method. Easier and awesome.

DIVISION BY NIKHILAM SUTRA

So, here is a new method for DIVISION by Nikhilam Sutra.. Hope you all like it.. Lets see who gets its logic first.

RECURRING DECIMALS

Hello guys, here is todays post. Its related to recurring decimals ending with 9 like 1/9 1/19 1/29 etc...
So the method goes as follows:
Steps:
1. The last digit will always be 1. eg 1/19= .1
2. The ratio of multiplication will be tens-1 ie 2 for 19, 3 for 29, 5 for 49 and so on.. Here for 1/19 -Ratio= 1:2
3. Start multiplying from the end and dont forget carry overs..
Continue till u get (number-1). So, here we must continue till we get 19-1=18
So, we have .9 4 7 3 6 8 4 2 1
Here after 8, we have 8*2=16. So 6 then 6*2+1=13 So 3. 3*2+1=7. 7*2=14 So 4. 4*2+1=9. 9*2=18!!! So stop here
4.Now complement the digits with 9 to the left.. means 1=8 2=7 3=6 and 4=5. So we get final answer as
0.052631578/947368421. So fast!!
Source: Ekadikha Purva
Examples:
1/29=0.03448275862068/96551724137931
1/49=0.020408163265306122448/979591836734693877551.
Try 1/69 1/79.. I am sure you will write within 3 minutes.
Lets see who gets this logic.. Its gonna be tough, very tough!!!

MULTIPLICATION BY BASES

Ok guys, here is todays post based on Multipilication by bases method..  

VEDIC CUBING

Hey guys this is my first post about VEDIC CUBING. Hope you all like it. Please feel free to share your views about the method. And lets see who is the first one to explain the logic behind the method:
Fabulous 2- digit cubing 

Steps: eg 12
1. Write first digit cube- 1
2. Write next 3 numbers in the ratio of digits- Here ratio is 1:2
So 1 2 4 8 
3. Double the middle two numbers and add them tothemselves
Here, 1 2 4 8
...........4 8.......
.....=1 7 2 8!!!!!!! Simple, isnt it
Source: The Anurupya Sutra
Examples:

1. 24^3= 8 16 32 64
..................32 64
............=13 8....2..4!!!

2. 32^3= 27 18 12 8
....................36 24
............= 32..7..6 8!!!

3. 38^3= 27 72 192 512
..................144 384
............=54 8......7.....2!!!!
This is based on a simple mathematical formula, lets see who decodes it.