Problematics | From Wonderland, without Alice

Oct 17, 2022 03:44 PM IST

Apart from his stories, Charles Lutwidge Dodgson aka Lewis Carroll, the author of Alice in Wonderland, created a number of delightful puzzles, one of which I have loosely adapted for you.

Lewis Carroll, a familiar name we associate with Alice in Wonderland, is actually a pseudonym. The author, whose real name was Charles Lutwidge Dodgson, was a mathematician who taught the subject at Christ Church College, Oxford.

Welcome to Problematics! (Shutterstock) PREMIUM
Welcome to Problematics! (Shutterstock)

Apart from his stories, Carroll/Dodgson created a number of delightful puzzles, one of which I have loosely adapted for you, making considerable changes to its surface as well as the numbers involved. This is to discourage anyone who might feel tempted to hunt the answer on the Internet. I shall name the original next week.

Puzzle 8.1 
Puzzle 8.1 
Puzzle 8.1 
Puzzle 8.1 
Puzzle 8.2 
Puzzle 8.2 
Mailbox: Last week’s solvers

#Puzzle 7.1

Hi Kabir,

Speed of the wagon = 13.5 km/hr = 3.75 m/s

Front wheel circumference = 2.5m

Rotations in 1 second (24 frames) = 3.75/2.5 = 1.5

Rotations in 1 frame = 1.5/24 = 1/16

Number of spokes = 16

So, spoke 1 will take the position of spoke 2, spoke 2 will take the position of spoke 3 etc... after 1 frame. It would look like the front wheel isn't moving at all.

Rear wheel circumference = 2.8m

Rotations in 1 second = 3.75/2.8 = 75/56

Rotations in 1 frame =75/(56*24) = (25/28)*1/16

Number of spokes = 16

So, spoke 1 will be a little behind in frame 2 compared where spoke 2 was in frame 1. It would look like the back wheel is moving backwards.

Loved today's puzzles. Harder, so more satisfying.

— Natrajan, Banaglore

#Puzzle 7.2


Opener #1 may have been running two runs, but must have failed to put his bat inside the crease and a short run must have been called. That’s why he was on strike although only one run was counted.

Match: Delhi Capitals vs Punjab Kings, 31st Match 2015

Opener #1: Virender Sehwag

— Aaryan Yashvardhan Sharma, IIT Ropar

Solved both puzzles: Ravinder Gahlout (Gurgaon), Natrajan (Bangalore), Geetansh (Delhi), Col (Dr) J S Sabharwal (Delhi), Shishir Gupta (Indore)
Solved #Puzzle 7.1: Anil Kumar Goyal (Delhi)
Solved #Puzzle 7.2: Nishant Bagga (Delhi), Rakshit Malik, Nipun Bamania, Vinay Bhatia, Aaryan Yashvardhan Sharma (IIT Ropar), Karan Sudarshan Sharma (Mohali), Mayobhav Pathak (Gurgaon), Sachin Pisharody (IP University, Delhi), Vinod Mahajan (Delhi), Onkar Singh (Delhi), Geetansha Gera (Faridabad), Jasvinder Singh (Nabha)

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

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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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