Coin and Matchstick Games: Important LRDI Questions for CAT 2026 Preparation

Coin and Matchstick Games are an important logical reasoning topic in CAT LRDI. These questions test your ability to identify patterns, apply game strategies, and think ahead instead of performing lengthy calculations. Once you understand the winning logic, such questions become quick and easy to solve.

Here, the given details explain the rules of coin and matchstick games, the 6k + 1 winning formula, and solved examples commonly asked in CAT. Practising these questions will strengthen your games and tournaments preparation and help you solve similar LRDI sets with confidence in CAT 2026.

What Are Coin and Matchstick Games in CAT LRDI?

Coin and matchstick games belong to the broader "games and tournaments" category tested in CAT. Unlike round-robin or knockout tournament questions, these games are based on two players picking coins (or matchsticks) from a table, one turn at a time, following a fixed set of rules. 

Such questions have appeared occasionally in CAT over the years and remain a useful practice area for strengthening logical reasoning and pattern recognition.

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Understanding the Game: Rules and Directions

Before solving any coin picking game question, it is important to understand the standard directions given in the question set:

• Two players, A and B, are playing a game that involves picking coin(s) from a table.

• Each player, on their turn, must pick a minimum of 1 coin and a maximum of 5 coins, except when only one coin is left, in which case that single coin must be picked.

• The game continues until all coins are removed from the table.

• Both players are intelligent and play with a strategy to win.

• The player who picks the last coin loses the game.

These five points form the base of almost every CAT LRDI question on this topic, so read them carefully before attempting any set.

The Winning Strategy: How to Never Lose This Game

The core idea behind solving coin and matchstick games is simple: since picking the last coin makes you lose, you must always leave your opponent in a position where they are forced to take that final coin.

Step 1: Find the Constant Sum

If the minimum pick is 1 and the maximum pick is 5, then the constant sum a player can maintain across two consecutive turns is:

Minimum + Maximum = 1 + 5 = 6

This means that whatever number of coins your opponent picks, you can always pick a corresponding number of coins so that the total picked by both players in that round equals 6. No other sum, such as 7 or 5, can be maintained consistently, since it would require picking 0 or more than 5 coins, both of which are not allowed.

Step 2: Identify the Safe Numbers

A "safe number" is the count of coins left on the table where, if it is your opponent's turn, you are guaranteed to win. Starting from the smallest case:

Every safe number is obtained by repeatedly adding 6 to the previous safe number, starting from 1.

Step 3: Generalise the Pattern

Observing this pattern in terms of number system fundamentals, all safe numbers follow the general form:

6k + 1

This is because the minimum and maximum sum (6) combines with the last single coin (+1) that the loser is forced to pick. If the number of coins left on the table is in the form of 6k + 1 and it is a player's turn, that player will lose the game, provided both players play intelligently.

How to Apply This Formula in CAT Questions

Once you know the 6k + 1 rule, solving CAT LRDI questions on this topic becomes a quick, mechanical process. 

Q1: If the game starts with 93 coins and it is A’s turn to pick up first, then how many coins should he pick to ensure his win? 

Q2: If the game starts with 157 coins and it is A’s turn to pick up first, then how many coins should he pick to ensure his win? 

Q3: If the number of coins to be picked by A is 2 in his first turn, in order to win the game irrespective of the number of coins that B wants to pick in his turn, then what can be the total number of coins on the table?

A. 146  B. 179  C. 97  D. 129

Why This Topic Matters for CAT 2026 Preparation

Coin and matchstick game questions are a good addition to LRDI practice because:

• They build logical and analytical reasoning skills useful across the exam.

• They require pattern recognition and generalisation, both tested extensively in CAT.

• They are relatively quick to solve once the formula is understood, helping save valuable exam time.

Students preparing for CAT 2026 should practise multiple variations of this game, including different minimum-maximum limits and different win/loss conditions, as part of a complete LRDI strategy for games and tournaments.