Your friend’s birthday is fast approaching, and there’s a slight problem—you’ve forgotten his age. While you know he’s older than one, his timeless appearance makes it hard to guess whether he’s two or two hundred. Adding to the complexity, your friend is a giant, and forgetting his age could have dire consequences for you.
The baker has crafted an impressive cake resembling a small mountain range, and your task is to sculpt the giant’s age in chocolate as the centerpiece. Counting the candles would be the obvious solution, but the cake is too tall for you to see the top. Fortunately, the baker has designed an interior tunnel that allows you to activate the candles from below. This gives you a chance to count them while the giant sleeps.
As night falls, you don a full bodysuit and prepare to navigate through vanilla cream. Inside the tunnel, you can see whether the candle above you is lit and have the ability to switch it on or off. The candles are arranged in a single loop, and in the darkness, you can’t discern the tunnel’s shape or size. With no tools or means to leave marks, you need a clever strategy to count the candles.
There are several ways to tackle this problem. The simplest method involves using the state of the candles to mark your position. You can light the first candle you encounter or leave it on. As you move forward, you’ll eventually find another lit candle. The challenge is determining whether it’s a new candle or the starting one.
One approach is to turn off the candle and backtrack to the start, counting the candles as you go. If the starting candle is off when you return, you’ve completed the loop and discovered the giant’s age. If not, continue to the next lit candle and repeat the process. This method will eventually work, but it could be time-consuming if many candles are lit, especially if the giant is older.
To find a more efficient solution, consider testing hypotheses about the giant’s age. Suppose you guess he’s turning 10. Light the starting candle, walk forward 10 candles, switch the destination candle off, and return. If the starting candle remains lit, 10 isn’t the answer. If it’s off, 10 could be correct, but it might also be a multiple of 10, such as 5 or 2.
To refine your guess, turn on all candles from 1 to 11, switch the 11th candle off, and return. The first unlit candle you encounter will indicate the exact number of candles. If no candles are extinguished, the total is higher than 10. Increase your guess systematically, perhaps by 4 each time. If there are 99 candles, this method would require 24 round trips and nearly 2,700 candle visits.
Instead of increasing guesses linearly, consider doubling them: 10, 20, 40, and so on. This approach allows you to reach high numbers quickly while starting with smaller intervals for fewer candles. After expecting a lengthy journey, you discover the giant is only turning 12. You quickly change into more appropriate attire, sculpt the chocolate numbers, and at the party, make a wish that you’re not downwind when your friend blows out his candles.
Imagine you are inside the tunnel of the giant’s cake. Create a simple game where you can simulate lighting and extinguishing candles. Use a piece of paper to draw a circle and place small objects (like coins) to represent candles. Practice counting and marking your position by turning the coins over. This will help you understand the strategy of marking and counting candles.
Write down different scenarios with a varying number of candles (e.g., 5, 10, 15). Use the method described in the article to determine the number of candles. Work through the problem step-by-step, and then check your answer by counting the candles directly. This will help you practice logical thinking and problem-solving skills.
Form small groups and discuss different strategies to count the candles efficiently. Role-play the scenario where one student acts as the giant, another as the baker, and others as the candle counters. This activity will help you understand the importance of teamwork and different approaches to solving a problem.
Write a short story or a diary entry from the perspective of the person counting the candles. Describe the challenges you face and how you overcome them. Use your imagination to add details about the giant’s birthday party. This will help you practice creative writing and empathy by putting yourself in someone else’s shoes.
Using the doubling strategy mentioned in the article, create a table to test different hypotheses about the giant’s age. Start with a guess and double it each time until you find the correct number. Record your findings and discuss how this method is more efficient than linear guessing. This will help you understand the concept of exponential growth and efficient problem-solving.
Counting – The action of finding the total number of items in a set by assigning a number to each item. – In math class, we practiced counting by twos to make it easier to add larger numbers.
Candles – Objects made of wax with a wick that can be burned for light or decoration, often used in celebrations. – For her birthday, we lit ten candles on the cake and counted them as we sang.
Strategy – A plan or method for achieving a specific goal, especially in problem-solving. – To win the game, we needed a good strategy to outsmart our opponents.
Puzzle – A game or problem that tests a person’s ingenuity or knowledge, often requiring critical thinking to solve. – We worked together to solve the math puzzle that challenged us to find the missing numbers.
Age – The length of time that a person has lived or a thing has existed, often measured in years. – My age is twelve, and I can use that information to help solve problems about how old I will be in five years.
Guess – To estimate or make a judgment about something without having all the information. – I had to guess the answer to the math question because I couldn’t remember the formula.
Efficient – Performing a task in the best possible manner with the least waste of time and effort. – Using a calculator made my math homework more efficient, allowing me to finish faster.
Solution – The answer to a problem or the way to solve it. – After working through the equations, we finally found the solution to the math problem.
Method – A particular way of doing something, especially a systematic way of solving a problem. – We learned a new method for dividing fractions that made it much easier to understand.
Critical – Involving careful judgment or evaluation, especially in thinking and problem-solving. – It is critical to check your work in math to ensure that your answers are correct.
