Video on vedic cubing

Here is a simple video that explains the concept of Vedic Cubing:

Vedic Cubing technique for 2-digit numbers.
https://www.youtube.com/watch?v=AOZtxkK0r1k

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...!!