Puzzle 110 - Solution

-

Answer : 4 units 

Area of a hexagon which is inscribed in a circle of radius r is 3 √3 / 2 * r2 

This hexagon has its side = radius of circle. 

But the circumscribed hexagon has radius of the circle as its perpendicular to a side from center of circle.  

 


 As shown in the diagram, if the side of outer hexagon is s, then the radius from center of circle perpendicular to the side, cuts the side in half. So the radius forms a right angled triangle with three sides as r, s/2 and hypotenuse as s.

Using Pythagoras theorem

s2 = r2  +s2 /4

3s2 /4 = r2 

s2  =r2 * 4/3

Now replacing this value for the area of outer hexagon, we get

area =  3 √3 / 2 *s2  =  3 √3 / 2* r2 * 4/3

But area of inner hexagon is 3 =>    3 √3 / 2* r2    is 3

Area of circumscribed hexagon = 3 * 4/3 = 4 units.  

Comments

Post a Comment

Popular posts from this blog

Puzzle 9 : The 4 coins problem

-
 Solution to puzzle 8: Maria is not counting Sundays. So she is not counting 1/7th of days of her age.  That is to say she is only counting 6/7th of her age. 6/7th of her age = 30 Her actual age = 30 X 7/6 = 210/6 = 35 years.  Puzzle 9 : The 4 coins problem  You’re creating a new coin system for your country. You must use only four coin values and you must be able to create the values 1 through 10 using one coin at a minimum and two coins maximum. What 4 coins do you choose, and can you think of a second set of 4 coins that achieves the same goal?
Read more

Puzzle 105 - Product of lcm and gcd

-
 What is the pair of numbers whose product is equal to the product of its least common multiple (LCM) and greatest common divisor (GCD)? You can find the solution here . Hint: The problem is much much easier than you think.  The GCD is the largest positive integer that divides each of two or more integers.   The LCM is the smallest positive integer that is divisible by both integers
Read more

Puzzle 13 - Alibaba's cave

-
Solution to puzzle 12: I am using brute force algorithm here. Let us start from the divisibility of 5. If two cards remain after dealing them for 5, the largest value less than 52 will be 47 If there are 47 cards and they are dealt to 3 people, 2 cards are left If they are dealt to 4 people 47 - 44 = 3 cards are left So 47 is the correct answer. Puzzle 13 : Alibaba's cave This puzzle is from mrbartonmaths Ali Baba found a cave full of gold and diamonds. A bag full of gold weighs 200 kilograms, a bag full of diamonds weighs 40 kilograms. Ali Baba can carry only 100 kilograms at a time. A kilogram of gold costs $20, and a kilogram of diamonds costs $60. What is the greatest amount of money Ali Baba can earn for the gold and diamonds he can carry out at once (in one attempt in one bag)?
Read more