Solve the puzzle by Mukul Sharma
Mukul Sharma is a multifaceted personality, having acted in films, run a pest control business, made TV serials, partnered an ad agency, produced front page pocket cartoons for The Telegraph newspaper and edited Science Today magazine for six years. He has written Dream Sequence, an anthology of science fiction short stories, among other works. He is a member of International Science Writers Association. He also has to his credit a weekly spiritual column for the Economic Times. But that's not why we are introducing him in these pages. He has been running a popular puzzle column Mindsport in a leading daily for many years now. Starting this issue, we bring to you a puzzle by Mukul Sharma every month. Pull up your socks for the mental jog

Puzzle for November Issue

Three players: A, B and C play a game using only the spades suit, ranging from the ace (counting as one) to the 10. These are shuffled and stacked face down upon the table. Each player in turn then draws a card, and this is repeated till the game terminates. On each occasion that s(h)e draws a card, the player must state the total number of pips in his or her hand; but some deception is permitted in that each player may, if s(h)e so wishes, tell just one lie in the course of the game. The winner is the first player who can correctly state which cards remain on the table. (Incidentally, these players are experts, and invariably claim the game as soon as it's possible to make the necessary deductions).

In one recent game the players drew in alphabetical order. A total of six cards were drawn. Their statements in chronological order were as follows. A: “7”; B: “8”; C: “8”; A: “14”; B: “17”; C: “10”.

As A reached out to draw the third card, B intervened. “Stop!” he said, “I can now tell you what cards remain on the table.” What were they?

— Answer will be published in the December issue

Last month puzzle and the answer

Your math class consists of six boys and six girls. In their annual exam, each has been awarded an integral mark out of 100. Disappointingly, no boy has received a distinction (over 80 per cent), but all the boys have managed over 40 per cent. The lowest mark in the class is 36.

Upon listing the boys' marks, you notice that all their marks are different prime numbers, and that their average is an even number. Further, three of the boys’ marks form an arithmetical progression (AP), and the other three another AP. Turning your attention to the girls, you find that their marks are all different. There is little overall difference in the performance of the sexes, the total of the girls’ marks being just one more than the total of the boys'. Three of the girls’ marks form one geometrical progression (GP), and the other three another GP with the same ratio as the first.

Finally, when listing the results in numerical order, you are pleased to see that Anjali who did so badly last year, has come seventh in the class. What were the top six marks (in descending order)?

Answer
One can get the boys' marks straightaway by listing all primes between 41 and 79. They are 41, 47, 53, 67, 73 and 79, summing up to 360. Thus total marks of girls is 361. The lowest marks in the class is 36 which a girl got. Now the marks of other girls are 36r, 36r^2, a, ar and ar^2, where 1 < r < 2 say r = p/q where q can take values 2, 3 or 6. Now checking all the values for p and q we get p = 3 and q = 2. Therefore, a = 40. Now the marks of all girls are as 36, 54, 81, 40, 60 and 90. Thus the top six marks are 90, 81, 79, 73, 67 and 60.