Recently, we had sent out a series of mails containing math puzzles, logical reasoning puzzles with discounts to our online course promised to those who solve the puzzles correctly (and provide the complete solution). We had also sent an email involving a creative thinking contest. All the mails and the details can be found below. You can send your solutions/answers to agastya@2iim.com or praveen@2iim.com; the last date for sending the solutions is this Sunday, 19^{th} of March. Students can make the purchases till Tuesday 21^{st} of March.

**Mail 1**

This email brings with it an “Earn your Discount” offer from 2IIM.

In this email we are going to outline three wonderfully engaging math problems. Two of these are routine while one is slightly tougher. Now on to the rules

- 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*

The questions, in no particular order of level of difficulty are as follows

- 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.
- A four-digit number ‘abcd’ is a perfect square. Further, we know that either the 2-digit number ‘ab’ is a factor or a multiple of ‘cd’. Find all possible values of a + b + c + d.
- [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [n/11] = [n/13].

**Mail 2**

This email brings with it the second “Earn your Discount” offer from 2IIM.

In this email we are going to outline three wonderfully engaging logical thinking problems. Two of these are routine while one is slightly tougher. Now on to the rules

- 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*

The questions, in no particular order of level of difficulty are as follows

- This one is an old classic. You have 12 bearings identical in size and appearance but one has a different weight (could be either light or heavy). You have a set of balance scales which will give 3 possible readings: Left = Right, Left > Right, or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter). You have only 3 chances to weigh the balls in any combination using the scales. Find which ball is the odd one and if it’s heavier or lighter than the rest. How do you do it?
- Give all numbers which when written in English have the letters appearing in alphabetical order. For instance, in the number ‘one’, the letters ‘o’ ‘n’ and ‘e’ are NOT in order. ‘o’ appears after in the English language and ‘e’ appears before ‘o’ and ‘n’
- Consider a bag that contains 100 white balls and 101 black balls. You play a game with the following rules. Pick two balls at a time,
- If both are black, replace with 2 white balls
- If both are white, replace with 2 black balls
- If one is white and one black, replace with one black ball

What is the probability that the last ball remaining is white?

**Mail 3**

This email brings with it the third and final “Earn your Discount” offer from 2IIM.

In this email we are going to take your help with naming one of the new products that we are building. We are in building an online course for middle-school kids that will teach them math differently. We want a really good name for the product/website and since name-selection seems like one of those activities where crowdsourcing works best, we want to take your inputs on this.

We have a set of rules and guidelines for name selection. The rules are sacrosanct and not to be broken, while the guidelines are similar to *directive principles of state policy* (go on, look it up). As in, take these seriously, but some gentle guideline-bending is not totally wrong.

**Rules**

- The domain name should exist. If you suggest math.com, it seems frightfully appropriate but chances are the domain was taken by someone aeons ago. A name without an available domain is useless. Go to Godaddy and check whether the domain is available
- Name should be short. Mathtaughtdifferently.com is ruled out.
- Spelling should be unambiguous. If you suggest choco.com, it could be chocko or choko as well. So, spelling ambiguity kills the name.

**Guidelines**

- Names that have six letters with three short syllables work best. Think ZOMATO, DOCOMO (IBACO is also good, even though there are only 5-letters)
- Alternating vowels and consonants work well. For instance WIZAKO is a good name.
- Name can have something to do with intuition, mathematics, learning, education, online in any language. But it is
that the name mean anything. Haagen Dazs means nothing, but sticks in the mind really well.__not necessary__ - Name should be easily pronounceable by people all over the world.

Reward

- The top 10 best names will get 10% discount on the online course
- Within these the best 3 names will get a discount of 20% on the online course
- The best name will get a special mention from us and a discount of 35% on the online course.

For more information on what this middle-school math course will contain, please visit http://school.piverb.com/

Best wishes for CAT Preparation. Crack these and avail the best discounts! To check out our CAT online course click here.

Cheers,

Rajesh