Imagine you’ve been on an epic adventure, following old maps and hearing tales of a hidden treasure. Finally, you find the legendary dungeon filled with ancient coins. The wizard who owns the castle is willing to let you take the coins, but there’s a catch: you must solve his tricky puzzle to leave the dungeon.
The puzzle seems simple at first. Each coin has two sides: one with a silver crest and the other with a gold crest. Your task is to split the coins into two piles, each with the same number of coins showing the silver side. Just as you’re about to start, the torches go out, and you’re left in complete darkness. You can’t see which coins are silver-side up anymore. However, you remember that there were exactly 20 silver-side-up coins before the lights went out. What can you do?
Here’s the trick: move 20 coins into a new pile, any 20 coins will do. Then, flip each of these coins over. That’s it! But why does this work?
Let’s break it down. You know there are 20 silver-side-up coins in total. When you move 20 coins to a new pile, you don’t know how many of those are silver-side up. Suppose you moved 7 silver-side-up coins. This means there are 13 silver-side-up coins left in the original pile. The remaining 13 coins in your new pile must be gold-side up. When you flip all the coins in the new pile, the 7 gold-side-up coins become silver-side up, matching the 13 silver-side-up coins in the original pile.
This solution works because of complementary events. Each coin can only be silver-side up or gold-side up. In any group of 20 coins, the number of silver-side-up and gold-side-up coins will always add up to 20. By flipping the coins in the new pile, you ensure both piles have the same number of silver-side-up coins.
Using algebra, if you move x silver-side-up coins to the new pile, the original pile has 20 – x silver-side-up coins left. The new pile, after flipping, will also have 20 – x silver-side-up coins, making both piles equal.
With the puzzle solved, the dungeon gate opens, and you escape with your treasure. But before you go, here’s another coin riddle for you. Imagine 8 different arrangements of coins. You can flip adjacent pairs of coins as many times as you want. A flip changes gold to silver and silver to gold. Can you figure out which arrangements can be made all gold?
Try solving this puzzle on the sponsor’s website, where you can explore interactive versions and confirm your solutions. This site helps you learn problem-solving by breaking puzzles into smaller parts and building up from there. You can sign up for free, and a premium membership offers even more puzzles. Visit the link provided to get a discount on the annual premium subscription fee for the first 833 visitors.
Gather 40 coins and a friend. Split the coins into two piles of 20. Have your friend randomly flip some coins in each pile. Now, try to solve the puzzle by creating two piles with the same number of silver-side-up coins, just like in the article. Discuss with your friend why the solution works.
Imagine you are the adventurer in the dungeon. Write a short story or script about how you solve the coin puzzle and escape with the treasure. Include dialogue and describe your thought process as you work through the solution.
Create a diagram or comic strip that illustrates the steps of solving the coin puzzle. Use drawings to show the initial setup, the process of moving and flipping coins, and the final result. Share your diagram with classmates to explain the solution.
Using algebra, explain why the solution works. Write equations to represent the number of silver-side-up coins in each pile before and after flipping. Present your findings to the class, showing how math helps solve the puzzle.
Visit the sponsor’s website mentioned in the article and try the interactive coin puzzles. Challenge yourself to solve different arrangements and see if you can make all coins gold. Reflect on how these puzzles enhance your problem-solving skills.
You heard the traveler’s tales, you followed the crumbling maps, and now, after a long and dangerous quest, you have some good news and some bad news. The good news is you’ve managed to locate the legendary dungeon containing the stash of ancient coins, and the eccentric wizard who owns the castle has even generously agreed to let you have them. The bad news is that he’s not quite as generous about letting you leave the dungeon unless you solve his puzzle.
The task sounds simple enough. Both faces of each coin bear the same crest, one in silver, one in gold. All you have to do is separate them into two piles so that each has the same number of coins facing silver side up. You’re about to begin when all the torches suddenly blow out, and you’re left in total darkness. There are hundreds of coins in front of you, and each one feels the same on both sides. You try to remember where the silver-facing coins were, but it’s hopeless. You’ve lost track. But you do know one thing for certain: when there was still light, you counted exactly 20 silver-side-up coins in the pile. What can you do? Are you doomed to remain in the dungeon with your newfound treasure forever? You’re tempted to kick the pile of coins and curse the curiosity that brought you here. But at the last moment, you stop yourself. You just realized there’s a surprisingly easy solution. What is it?
Pause here if you want to figure it out for yourself.
You carefully move aside 20 coins one by one. It doesn’t matter which ones; any coins will do, and then flip each one of them over. That’s all there is to it. Why does such a simple solution work? Well, it doesn’t matter how many coins there are to start with. What matters is that only 20 of the total are facing silver side up. When you take 20 coins in the darkness, you have no way of knowing how many of these silver-facing coins have ended up in your new pile. But let’s suppose you got 7 of them. This means that there are 13 silver-facing coins left in the original pile. It also means that the other 13 coins in your new pile are facing gold side up. So what happens when you flip all of the coins in the new pile over? Seven gold-facing coins and 13 silver-facing coins to match the ones in the original pile.
It turns out this works no matter how many of the silver-facing coins you grab, whether it’s all of them, a few, or none at all. That’s because of what’s known as complementary events. We know that each coin only has two possible options. If it’s not facing silver side up, it must be gold side up, and vice versa. In any combination of 20 coins, the number of gold-facing and silver-facing coins must add up to 20.
We can prove this mathematically using algebra. The number of silver-facing coins remaining in the original pile will always be 20 minus however many you moved to the new pile. And since your new pile also has a total of 20 coins, its number of gold-facing coins will be 20 minus the amount of silver-facing coins you moved. When all the coins in the new pile are flipped, these gold-facing coins become silver-facing coins, so now the number of silver-facing coins in both piles is the same.
The gate swings open, and you hurry away with your treasure before the wizard changes his mind. At the next crossroads, you flip one of your hard-earned coins to determine the way to your next adventure. But before you go, we have another quick coin riddle for you – one that comes from this video sponsor’s excellent website.
Here we have 8 arrangements of coins. You can flip over adjacent pairs of coins as many times as you like. A flip always changes gold to silver, and silver to gold. Can you figure out how to tell, at a glance, which arrangements can be made all gold? You can try an interactive version of this puzzle and confirm your solution on the sponsor’s website.
We love this site because it gives you tools to approach problem-solving in one of our favorite ways—by breaking puzzles into smaller pieces or limited cases, and working your way up from there. This way, you’re building up a framework for problem solving, instead of just memorizing formulas. You can sign up for free, and if you like riddles, a premium membership will get you access to countless more interactive puzzles. Try it out today by visiting the provided link and use that link so they know we sent you. The first 833 of you to visit that link will receive a discount on the annual premium subscription fee.
Coins – Flat, typically round pieces of metal used as money, often used in math problems to teach counting and value. – Example sentence: “If you have 5 coins and each is worth 10 cents, how much money do you have in total?”
Silver – A precious metal often used in coins, which can be used in math problems to discuss value and weight. – Example sentence: “The silver coin weighs 5 grams, and we need to calculate the total weight of 10 such coins.”
Gold – A valuable metal often used in math problems to explore concepts of value and comparison. – Example sentence: “If a gold bar is worth $500 and a silver bar is worth $100, how many silver bars equal the value of one gold bar?”
Pile – A group or stack of objects, often used in math to discuss grouping and counting. – Example sentence: “There is a pile of 20 blocks, and we need to divide them equally among 4 students.”
Flip – To turn over or change position, often used in probability problems involving coins. – Example sentence: “If you flip a coin, what is the probability that it will land on heads?”
Number – A mathematical object used to count, measure, and label, fundamental in all areas of math. – Example sentence: “Choose a number between 1 and 10 and multiply it by 2.”
Algebra – A branch of mathematics dealing with symbols and the rules for manipulating those symbols. – Example sentence: “In algebra, we often solve for the unknown variable in an equation.”
Solve – To find the answer to a problem or equation. – Example sentence: “Can you solve the equation 3x + 5 = 20 for x?”
Puzzle – A problem designed to test ingenuity or knowledge, often involving mathematical concepts. – Example sentence: “The math puzzle required us to find the missing number in the sequence.”
Arrange – To put in a specific order or pattern, often used in math to discuss sequences and patterns. – Example sentence: “Arrange the numbers 3, 1, and 2 in ascending order.”
