Solve Cash in a Bag Logic Puzzle: Master Logic based on Reasoning

Submitted by Atanu Chaudhuri on Sat, 22/03/2025 - 06:08

Cash in a Bag Logic Puzzle

The Cash in a Bag Riddle—a Primer on Reasoning and Logic Analysis

Learn how to solve the Cash in a Bag logic puzzle with this step-by-step guide. Master logic based on reasoning and sharpen your problem solving skills!

The Cash in a Bag Tricky Logic Puzzle

Three bags with messages "The Cash is not here", "The Cash is not here", and "The Cash is in the middle bag" written on them are placed left to right. Cash is in one bag. If one message true and the rest false, which bag has the Cash?

Time to solve: 5 minutes.

Hint: Apply reasoning and logic analysis.

Solution of Cash in a Bag Logic Puzzle

Understand the puzzle

Three bags with three messages on them:

Left bag: The Cash is not here.
Middle bag: The Cash is not here.
Right bag: The Cash is in the middle bag.

One of the messages is true, the other two false.
Find which bag has the cash.

Solutions to the Cash in a Bag Logic Puzzle

Use reasoning to analyze the right bag first, examining consequences of truth or falsity of the message. A schematic of the bags will help in your analysis.

three bags schematic

Strategy adopted by reasoning: Analyze first, the message on the right bag as it holds maximum information by referring to one other statement. Rest of the messages refer to only its own bag.

Reasoning is vastly different from Logic in its scope. Reasoning allows use of prior experience to choose and apply the strategy or problem solving techniques most effective for solving the problem you face.

The Reasoning Logic widely known to aid quick solution:

In analyzing a collection of statements logically, choose first the statement containing maximum amount of information, usually the statement that refers to most number of other statements among all.

Justification: By analyzing one, get the advantage of examining the other statements together with the first.

Result: More effective and faster decision arrived at one go. Overall uncertainty reduces considerably with many promising information discovered by the first analysis itself.

Solution by Analyzing Possibilities and Consequences for the Rightmost Message

Case 1: Right message "Cash is in 2nd bag": True.

Implies: Cash is actually in the middle bag,
Middle message "Cash is not here": False (because of truth of right bag message, Cash is actually in the middle bag).
Left message "Cash is not here": True (because Cash is actually in middle bag).
As only one statement can be true by puzzle condition, the assumption that right bag message is true can't be correct. The message must be wrong.

Case 2: Right message "Cash is in 2nd bag": False.

Case 2.1: Cash in the right bag:

Middle message "Cash is not here": True.
Left message "Cash is not here": also True.
As only one message can be True, the assumption that "Cash in the right bag" can't be correct. Cash can't be in the right bag.

Case 2.2: Cash in left bag:

Middle message "Cash is not here": True.
Left message "Cash is not here": False.
With only the middle message True, and the other two False, the assumption that Cash is in left bag satisfies all puzzle conditions and is the solution.

⇨ Answer: Cash is in the left bag.

All possibilities of the message on the right bag and the consequences analyzed systematically to get the answer in fewest steps.

This is possible by adopting the well-known strategy and rigorous logic analysis.

Solution by Common-sense Plain English Reasoning and logic

I identify an interesting pattern of left and middle bags both deny having the cash. By puzzle conditions, both can't be true.

So, the cash must be either in left or in the middle bag.

Ultimately, if the message in the middle is true, it automatically makes the right bag message also true, This is not valid by puzzle conditions.

So, the message in the middle cannot be true, and the cash lies in the left bag all along.

Solution by Visual Logic Analysis and Reasoning Strategy

Using reasoning in logic analysis of a collection of statements, choose the rightmost message carrying maximum amount of information.

Visual logic analysis of Cash in a bag riddle

Strategic logic analysis: Without strategy, use of logic is inefficient—has little practical value. In solving this puzzle also a major strategy is used in each solution—namely, analyzing first the statement that carries maximum information. This particular strategy helps to guide the overall process of analyzing a collection of condition statements efficiently avoiding random statement choices without any direction. This is strategic logic analysis.

Questions for you

Which of the three solutions you like most, and why?
Do you always think in strictly logical manner while going through life?
What happens if you apply logic in your every action?
Is it really important to use logical reasoning wile facing any problem in your life?
Do you consider in conjuring up three solutions to a simple logic puzzle, I have made things unduly complex?
Do you think simplicity and logic are in conflict with each or complexity and logic in conflict?
What is your opinion—all around you simplicity rules, or complexity?
Do you find the human civilization largely conforms to logical reasoning?