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Dec 12, 2022 05:24 PM IST

When someone identifies an error in someone else’s puzzle, it is called “cooking” the puzzle. Here's a simplified adaptation for readers of Problematics!

Type “America’s greatest puzzle creator” into Google’s search box and you will find the name of Sam Loyd filling your results page. For all his genius, however, Loyd (1814-1911) was as vulnerable as any of us when it came to making mistakes.

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

When someone identifies such an error in someone else’s puzzle, it is called “cooking” the puzzle, to use a term I first came across in Martin Gardner’s Mathematical Carnival. Gardner’s book describes how he cooked a puzzle for which Loyd himself had given a wrong answer. The following is my adaptation, simplified to an extent and customised for readers of Problematics.

Problematics Week 16!
Problematics Week 16!
#Puzzle 16.1.
#Puzzle 16.1.
#Puzzle 16.2:
The speed at which I write varies depending on how tough the subject is. Running a stopwatch, I marked the moments when I completed ¼, ½, ¾ of this column, and finally at the end. Starting at 1 pm, I completed the third quarter at 2:07:30. I spent an equal amount of time writing the first and the second halves. Also, the last quarter took me exactly the same time as the third. How much time did I spend writing? 

# Puzzle 15.1 

Hi Kabir, 

We first analyse the top two hands of poker. 

Straight flush: Number of possible straight flushes in one suit = 10 (A-2-3-4-5, 2-3-4-5-6, 3-4-5-6-7, ... 10-J-Q-K-A). Number of possible straight flushes across all suits = 4 x 10 = 40 

Four of a kind: Let's take aces. Number of ways one gets 4 Aces in a 5-card draw = 48. This is because you can pick any of the 48 cards as the fifth card and one way of picking the remaining 4 cards. Total number of ways for four of a kind in entire deck = 48 x 13 = 624 

This means a straight flush is 624/40 = 15.6 times less likely to happen than four of a kind. 

So, poker's ranking system is correct. 

Trio: In teen patti, let's take aces. Number of trios of aces possible = 4 (you can pick 3 aces from 4 suits in 4 different ways). Number of trios possible in teen patti = 13 x 4 = 52 

Straight flush: Number of straight flushes possible per suit = 12 (A-2-3, 2-3-4, 3-4-5..., J-Q-K, Q-K-A). Total straight flushes possible across suits = 12 x 4 = 48 

This shows the probability of a straight flush is lower than that of a trio. Therefore, teen patti's ranking system is flawed

The answer is that poker's ranking system is good and teen patti's is flawed. 

Rahul Agarwal, Bay Area, California

#Puzzle 15.2

Hello Kabir, 

This one seems the easier of the two. Henry already has three 3s. Lonnegan has two 9s. The order of the remaining deck should be (top down) 3N99. N is the null card. 

* If by any chance Henry discards & draws (DND) nothing, Lonnegan would DND 3 (result: Henry three 3s, Lonnegan three 9s). 

* If Henry DNDs 1, Lonnegan DNDs 3 (Henry four 3s, Lonnegan four 9s). 

* If Henry DNDs 2, Lonnegan DNDs 2 or even 3 (Henry four 3s, Lonnegan four 9s

* Unlikely, but if Henry were to DND 3, Lonnegan DNDing 1, 2, or 3, doesn’t matter (Henry three 3s, Lonnegan three 9s). 

Need to go watch The Sting once again. One of my long-time favourites. 

Sanjay Gupta, Delhi 

A number of solvers have got their answers wrong this week. Madhuri Patwardhan of Thane approaches #Puzzle 15.1 the right way but makes a miscalculation in the process. Akshun Gulati of Delhi gets it right on the second attempt. 

Rahul Agarwal and Rituparna Gupta are the only ones who have solved both puzzles correctly. Other than them, only Sanjay Gupta gets #Puzzle 15.2. 

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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