Problematics | The colours of mathemagic

Problematics | The colours of mathemagic

There is no reason why our puzzles should be topical. For example, just because this is election season does not mean we should scratch our heads over an Einstein puzzle about which candidate driving which car is being fielded from which seat by which party.

Representational Image

On the other hand, some occasions do call for topical puzzles. Such as a movie puzzle during the Oscars, or a cheetah puzzle when the cats were first released into the Indian wild. Or on a festive occasion like this one. Have a Happy Holi solving this week’s puzzles.

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#Puzzle 83.1

On a table, a magician lays out three packets of Holi colours — one red, one green and one yellow — and an open box containing two dozen sweets. He then invites an audience of three dummies to sit on the table.

Turning his back, the magician tells the 3 Idiots: “Each of you take a packet of colour and put it in your pocket.”

That done, the magician turns around to face the three, and then proceeds to hand them sweets from the box. One sweet to Dummy #1, two sweets to Dummy #2, and three sweets to Dummy #3.

Turning his back again, the magician gives further instructions:

(a) “Each of you take a few more sweets as instructed below:

(b) “The person who pocketed the red packet, you take as many sweets as I gave you;

(c) “The person who pocketed the green packet, you take twice as many sweets as I gave you; and

(d) “The person with the yellow packet in your packet, you take four times as many sweets as I gave you.”

“Done,” chorus the 3 Idiots.

The magician then turns around once again to face his audience, takes one look at the sweets remaining in the box, and announces:

“You have red, you have green, and you, sir, have yellow.”

How is it done?

#Puzzle 83.2

Puzzle 83.2
Puzzle 83.2

Just because it’s Holi, let’s tamper with the Wordle rules just a little bit:

(a) As in the typical game, the hidden word contains five letters;

(b) As in the typical game, again, a green square means the letter appears in the hidden word in exactly the same position; and

(c) In yet another rule unchanged from the typical game, again, a yellow square means the letter appears in the hidden word, but in a different position. However,

(d) Unlike in the typical game, there are no grey squares to tell you which letters do not appear in the hidden word at all. Rather, it’s a bright Holi red that identifies the letters missing in the hidden word.

What is the hidden word in the illustrated game?


##Puzzle 82.1

Hi Kabir,

I am really hooked to these puzzles. I am on vacation but still trying to answer them.

The crow should pick garbage from the midpoint of where it is sitting and its nest so as to form an isosceles triangle while flying.

— Dr Sunita Gupta

#Puzzle 82.2


The fractions are as follows:

1/3 = 5832/17496 = 5823/17469

1/4 = 3942/15768 = 4392/17568

1/5 = 2697/13485 = 2769/13845

1/6 = 2943/17658 = 4653/27918

1/7= 2394/16758 = 2637/18459

1/8 = 9541/76328 = 9523/76184

1/9 = 6381/57429 = 6471/58239

— Ajay Ashok, Mumbai

The first puzzle was really a sitter although some readers introduced unnecessary complications. In fact, I had omitted a key point and made it even simpler. We wil get back to a different version some other time.

The second puzzle, of course, has multiple solutions. I am crediting everyone who has got at least six of the seven required fractions.

Solved both puzzles: Dr Sunita Gupta (Delhi), Ajay Ashok (Mumbai), Yadvendra Somra (Sonipat), Akshay Bakhai (Mumbai), Group Captain RK Shrivastava (retired, Delhi),

Solved Puzzle #82.1: Sampath Kumar V (Coimbatore), Kanwarjit Singh (Chief Commissioner of Income Tax, retired)

Solved Puzzle #82.2: Shishir Gupta (Indore)

Problematics will be back next week. Please send in your replies by Friday noon to

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