AFTER the Agra summit has failed to resolve their differences, President Pervez Musharraf and Prime Minister Atal Behari Vajpayee decide to give peace another chance. The dialogue proceeds... as follows: "General, I still believe that we have been talking on parallel lines only, so far," "Yes Mr Prime Minister, and you know that parallel lines never meet." "Chief Executive, parallel lines do meet — at infinity — and we can reach there if we proceed in a cool and calculated manner." "However, Vajpayee ji, being a soldier, I face issues square up." "How do we face this one square up, Mr President?" "In a calculated manner, as you have suggested, Atal ji." "Do you mean that we decide it over a game of mathematics?" "Precisely, Mr PM."

"I should warn you that His Excellency the President of Pakistan is a brilliant mathematician," Pakistani Foreign Minister Abdul Sattar whispers across the table to his Indian counterpart Jaswant Singh, who says, "Atal ji also knows how to reach the magic figure." "Aha! the magic figure, meaning infinity?" "No, 272." "Does that give you a surprise result?" "No, only a simple majority in the Parliament." Meanwhile, the contest has begun. "Mr PM, I found this problem in a book. It says that digits from 1 to 9 are to be arranged in three rows and three columns in such a way that the resultant matrix contains a maximum number of figures (read horizontally, diagonally or vertically) that are perfect squares. My answer to this is that the maximum number of possible squares is 10.

812

465

937; It contains these squares: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 361." "Our views on this are almost similar, Chief Executive, but the solution that I have in mind is:

812

365

497; It has 1, 4, 9, 16, 25, 36, 49, 81, 169 and 961." "I still say that my solution is better and we have reached a dead end again, Mr PM." "Wait, Mr Jaswant has come up with a revised draft. It says that the maximum possible squares are 11.

729

546

831; It has 1, 49, 36, 4, 64, 9, 169, 16, 961, 25 and 729. Does that change the position?" "No, because, we, too, have revised our draft, which gives 11 squares.

183

652

947; It has 81, 169, 961, 256, 25, 16, 49, 64, 9, 4 and 1." "Mr President, we would like to change the draft again because it has just occurred to me that the maximum possible squares are 12.

169

324

758; It has 1, 4, 9, 16, 25, 36, 49, 64, 169, 324, 625 and 961." "I object to this constant redrafting, but, my team, too, has a solution for 12 squares, which is different than yours.

841

526

739; It has 1, 4, 9, 16, 25, 36, 64, 169, 324, 625, 841 and 961. I insist that this is the correct one." "Chief Executive, we have similar solutions to the same problem; the only difference is in our respective points of view." "However, Atal ji, the core issue remains unresolved, so, there can be no joint declaration, but I invite you to Lahore to continue the dialogue." "I accept your invitation Mr President and I am sure we'll find out a solution by the next summit." There are 22 possible squares in this problem (1, 4, 9, 16, 25, 36, 49, 64, 81, 169, 196, 256, 289, 324, 361, 529, 576, 625, 729, 784, 841 and 961), only 15 of which can possibly coexist. We’ll have to find out a solution before the next summit.

— Aditya Rishi