14 thoughts on “Chessboard Conundrums – CAT Scan

  1. Hi J though it is not yet confirmed by iim Indore about the exact no of questions can you please do a post on the probable changes.also how should be change our strategy at this point for the same.

    • No point, to be honest, without more info. Your guess is as good as mine at this point. Would say this much – the currculum is the same, the concepts are the same, the CAT-skills therefore are the same. CAT has changed many times over the years (and with much less warning, in the paper-based days) but the skills needed to ace it have remained remarkably consistent. Strategy might need to be be tweaked a bit, that’s all, and we don’t have enough info yet to speculate meaningfully on the details of that (though I am sure you will find plenty of equally clueless people willing to give gyaan).

      Frankly, yeh sab moh maaya hai; as long as the changes are the same for everybody, all you would need to do is to stay calm and be prepared.


  2. Hi J, this is off-topic. But, I am trying to remember a property with proof rather than mugging it straight up so that it stays in my long-term memory. Why is for f(x+y)=f(x)f(y), the function a exponential function of the form a^x? I tried across the internet for a calculus based proof but couldn’t find any, not even a graph for the same. Can you help me please?

    • The important thing here is it behaves the same way as an exponential – a^m * a^n = a^(m+n). It may not be precisely provable to be an exponential, but if it looks like a duck and it quacks like a duck, let’s call it a duck…


  3. How can we calculate something like the probability that black wins in two moves (Fool’s mate) or white wins in four moves (Scholar’s mate)?

    P.S. Consider them as separate questions.

    • Depends on your assumptions. If nothing specified you would need to take all possible sequences of 4 moves (2 each) type of thing. Totally out of scope for any exam. Don’t waste time on it.


  4. Hi J. The usual way out of putting the value as a “constant” for finding the max/min value of quad/quad form and then solving it by deriving an equation in it is too cumbersome. I’m extremely comfortable with differentiation, so can you please suggest how to find the quad/quad form’s max or min value by differentiation? I’d be grateful to you for this. 🙂

      • Thank you for the quick reply. Although, I’m already aware of finding the max/min value of a quadratic to compute the value of x at which max/min would occur through differentiation. And plugging it back in the equation indeed gives the correct value of the function, since the differentiation wrt to x is nothing but x=-b/2a of a quadratic ax^2 + bx + c. But, the problem arises when we have to maximize, let’s say (2x^2 + 4x + 5) / (4x^2 + 7x + c). If I straight in differentiate each equation individually and then divide their respective values of the function, the answer is wrong by billions. I’m failing to understand why differentiation isn’t working here, whereas assuming the whole thing as K and then going to solve it for K results in a correct value 😦

  5. Because finding the minimum of P/Q is not the same as finding the minimum of P upon the minimum of Q. Moreover, when you split it, the respective minima may come at different values of x while for the overall (P/Q) there will be a single value at which it become minimum.


  6. Hi J, in an exam scenario, making boxes and trying to figure out the answer could take some time. what was your approach when you had attempted this set? or was it fairly easy for you given the fact you are comfortable with the game and the board.

    • I can make the boxes pretty fast, and after that familiarity helps (I was also able to reuse the boxes by using different notations, so had to draw just 2 (last question didn’t need a drawing). I was in the other slot, but when I did attempt this slot later, this whole set took me around 5 minutes.


  7. Ahaan! right, using numbers instead of just crossing boxes out in Q2 would have helped in reducing the solving time.

    Thank you, J 🙂

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