Recently, we had sent out a mail containing 3 puzzles with discounts to our online course promised to those who solve the puzzles correctly (and provide the complete solution). The mail and the details can be found below. You can send your answers to rajesh@2iim.com; the last date for sending the solutions is midnight of April 12th.

**Contents of the Mail**:

Have you ever thought “How can we make this CAT preparation gig more fun?”. If you have not yet thought about this, you should. Luckily enough for you, we have.

- We give you three questions/puzzles in this email. If you get 1 or more right, you are eligible for discounts. Students who get 1 of the puzzles right will be eligible for a discount of 10%. Those who get 2 of these correct will be eligible for a discount of 20%. Those who get all three correct will get a discount of 35% on our Green and Comprehensive Courses.
- Discounts will be offered
if detailed explanations are provided for the questions. Merely pointing out some answer is insufficient.*only*

__All about primes__:

Prime numbers have fascinated human beings forever. There are twin primes, cousin primes, cullen primes, beastly primes, palindromic primes, absolute primes, circular primes and a gazillion other variants. These are absolutely fabulous things to think about. So, let us step into puzzle 1. We want the smallest 5-digit snowball prime. Hand that over promptly and you can avail a 10% discount.

Puzzle 2 is tougher. There are 2-digit prime numbers ‘ab’ such that the prime number is the (a*b)th prime number. For instance, 17 is the 7^{th} prime number and 73 is the 21^{st} prime number. This is why some folks call 73 as the best number in the world, but that’s a discussion for another day. There is no three digit number ‘abc’ that is (a*b*c)th prime. However, there is/are perhaps one(or more) 3-digit number(s) ‘abc’ that is the (a*b*c)th odd prime. Give all possible such 3-digit prime numbers and pat yourself on the back. If you find this by brute force without resorting to the computer, then you should go and get yourself a giant ice-cream as well.

__Let us think Geometry__:

Each triangle has 3 angles and 3 sides. If there were two triangles that have their corresponding three angles and three sides equal, then these two are congruent. This much we know. Now, what is the maximum number among these 6 metrics – 3 angles and 3 sides – that can be equal between two triangles and the triangles still be non-congruent. To be more explicit, we can have two triangles measuring 5, 6, 7 and 5, 6 and 8. These two have one side equal and are still not congruent. We can have 2 triangles with angles 80-40-60 but with different sizes – these two are also non-congruent. Provide two triangles that have the maximum number of metrics identical but are still not-congruent and then step aside for said ice-cream.

As the saying goes, kids discuss congruence, adults discuss similarity, legends discuss non-congruence.

Kindly send your responses to rajesh@2iim.com on or before midnight April 12^{th} to avail discounts.

Those of you who do not have the slightest interest in availing discounts, please try these puzzles. We would love to discuss these puzzles and chat about them with like-minded folks. Discount is merely the cherry on top of the cake.

Best wishes folks and happy solving!

Cheers,

Rajesh