Here’s a fun riddle for you to solve! Imagine you have 12 marbles. Out of these, 11 marbles are exactly the same, and one is different because it weighs either more or less. Your task is to find out which marble is different, but you can only use a balance scale three times. Ready to give it a try?
Start by placing 4 marbles on one side of the scale and 4 marbles on the other side, leaving 4 marbles off the scale. This is your first weighing. Two things can happen: the scale is either balanced or unbalanced.
If the scale balances, the odd marble is among the 4 marbles you didn’t weigh. Now, weigh 3 of those unweighed marbles against 3 marbles you know are normal. If the scale balances again, the fourth unweighed marble is the odd one. Weigh it against a normal marble to see if it’s heavier or lighter.
If the scale is unbalanced, the odd marble is among the 3 you just weighed. Weigh two of these marbles against each other. If they balance, the third marble is the odd one. If they don’t balance, the heavier or lighter one is the odd marble.
If the first weighing is unbalanced, the odd marble is among the 8 marbles on the scale. You still don’t know if it’s heavier or lighter. Let’s say the left side is heavier. This means the odd marble is either one of the 4 on the heavy side or one of the 4 on the light side.
Now, weigh 3 marbles from the heavy side and 1 marble from the light side against 3 normal marbles and 1 marble from the heavy side. If the scale balances, the odd marble is one of the 3 light-side marbles not on the scale. Weigh one of these against another. If they balance, the third marble is the odd one. If they don’t, the lighter one is the odd marble.
If the second weighing is unbalanced, and the side with 3 normal and 1 heavy-side marble is heavier, then the odd marble is either the heavy-side marble or the light-side marble on the other side. Weigh the heavy-side marble against a normal marble to find out.
If the second weighing is heavier on the 3-heavy-side and 1-light-side marbles, the odd marble is one of the 3 heavy-side marbles. Weigh one of these marbles against another. If they balance, the third marble is the odd one. If they don’t, the heavier one is the odd marble.
To solve this riddle, you use both deductive and inductive reasoning. Deductive reasoning helps you make decisions based on what you know, like weighing 4 marbles against 4 marbles to see what happens. Inductive reasoning helps you figure out what to do next based on the results, like deciding which marbles to weigh next.
We use these types of reasoning in everyday life, like figuring out what time to leave to get somewhere on time. By practicing with puzzles like this, you can get better at solving problems and making decisions in real life!
Imagine you have a set of 12 marbles, just like in the riddle. Use a simple balance scale simulation online or create a physical model using a ruler and some small objects. Try to find the odd marble by following the steps outlined in the article. This hands-on activity will help you understand the logic behind each weighing.
Create your own logic puzzle similar to the marble riddle. Think of a scenario where you need to find an odd item among a group using limited attempts. Share your puzzle with classmates and see if they can solve it. This will enhance your creative thinking and problem-solving skills.
Discuss with your classmates how deductive and inductive reasoning were used in solving the riddle. Share examples of how you use these types of reasoning in everyday life. This activity will help you recognize and apply logical reasoning in various situations.
Write your own riddle that involves using logic to solve a problem. Exchange riddles with a partner and try to solve each other’s challenges. This will improve your ability to think critically and creatively.
Think of a real-life problem you face regularly, like organizing your study time or planning a route to school. Use deductive and inductive reasoning to come up with a solution. Share your approach with the class and get feedback. This will help you apply logical reasoning to practical situations.
Here’s a sanitized version of the provided YouTube transcript:
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This is a riddle, and I need your help to solve it. Let me explain: I have 12 marbles, 11 of which are identical, and one that looks the same but weighs a slightly different amount. I need to figure out which marble is different. I have a scale I can use to compare groups of marbles, but I can only use it three times. Additionally, I don’t know whether the odd marble weighs more or less than the others. How can I find the different marble?
To try figuring it out for yourself, pause the video on the next screen. This is known as the 12-marble problem. To solve this, let’s start by weighing 4 marbles against 4 marbles, leaving 4 off the scale. This is our first weigh, and it can go one of two ways: either the scale is balanced, or it’s not.
If the scale is balanced, we know that the odd marble is in the other 4, and that the 8 on the scale are all normal. Next, we can weigh 3 verified normal marbles against 3 marbles from the questionable group. If this is balanced, we know the fourth marble is the odd one, and we can weigh it against a normal one to find out if it weighs more or less than the others. If the three and three aren’t balanced, however, then we know whether the odd marble weighs more or less than the others, and that it’s in that group of three.
Next, weigh two of those marbles against each other. If they’re the same, you know the third marble is different. If they’re different, you know which one is the odd marble.
But what if the first time you weigh four marbles against four marbles they’re different? You know that the odd marble is one of eight, and you still don’t know if it’s heavier or lighter than the rest. If it’s heavier, it’s one of the 4 on the heavy side, and if it’s lighter, it’s one of the four on the lighter side. You also have 4 marbles you know are normal and only two weighs left.
Here’s the trick: weigh three “heavy-side” marbles and one “light-side” marble against three normal marbles and one “heavy-side” marble. If it’s balanced, you know the odd marble is lighter than the others, and it’s one of the 3 “light-side” marbles not on the scale. Weigh one of those marbles against another. If it’s not balanced, the lighter one is the odd marble. If it is balanced, then the third marble is the odd one.
What if your second weigh isn’t balanced? If it’s heavier on the 3-normal and 1-heavy-side side, then you know either the 1 heavy-side marble is the odd one and is heavier than the others, or the 1 light-side marble on the other side is the odd one and is lighter than the others. Weigh the heavy-side marble against a normal marble to find out.
If the second weigh is heavier on the 3-heavy-side and 1-light-side marbles side, then you know the odd marble is heavier than the others and is one of the 3-heavy-side marbles. Weigh one of those marbles against another. If it’s balanced, the third is your heavy odd marble. If it’s not balanced, the heavier one is the odd marble.
Getting to this solution can take a number of different paths. You could brute-force a solution by trying any and every possible combination of weighs until you found a sequence that works, but this doesn’t sound very elegant or efficient. More likely, you’d want to use both inductive and deductive reasoning to design your solution.
Deductive reasoning is “top-down” logic. For example: if I weigh four marbles against four marbles, what does that tell me? Inductive reasoning, on the other hand, is bottom-up. In this problem, that’s a question like: if I have 3 marbles left, and I know if the odd marble is heavier or lighter than the rest, then I can solve it in 1 weigh. So how do I get from 4 possibly heavy, 4 possibly light, and 4 normal to there?
We use deductive and inductive reasoning all the time in real life. “If I leave at 5:30, what time will I get there?” and “If I have to arrive by 6, what time do I have to leave?” are just two simple examples. Practicing this form of logic in marble-finding thought puzzles can help us get better, faster, and more efficient at using that logic in other situations.
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This version removes any informal language and maintains a clear, structured presentation of the riddle and its solution.
Marbles – Small, round objects often used in games or as counters in mathematical problems. – In our math class, we used marbles to help us understand probability by drawing them from a bag.
Scale – A tool used to measure weight or mass, often used in experiments and problem-solving. – We used a scale to weigh different objects and compare their masses during the science experiment.
Weighing – The process of measuring the weight or mass of an object. – Weighing the marbles helped us determine which one was heavier without using a scale.
Odd – In mathematics, a number that is not divisible by 2. – When we added the two odd numbers, the result was an even number.
Balanced – In equilibrium; when two sides of an equation or scale are equal. – The teacher showed us how to keep an equation balanced by adding the same number to both sides.
Unbalanced – Not in equilibrium; when one side of an equation or scale is not equal to the other. – The scale was unbalanced because we placed more marbles on one side than the other.
Reasoning – The process of thinking about something in a logical way to form a conclusion or judgment. – Critical thinking and reasoning are important skills when solving complex math problems.
Deductive – A type of reasoning that starts with a general statement and reaches a specific conclusion. – Using deductive reasoning, we concluded that if all squares are rectangles, then a particular square must also be a rectangle.
Inductive – A type of reasoning that involves making generalizations based on specific observations. – By observing several patterns, we used inductive reasoning to predict the next number in the sequence.
Problem-solving – The process of finding solutions to difficult or complex issues. – We practiced problem-solving by working through challenging math puzzles in groups.
