Maths Problem: Finding Mahmud's Apples

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Hey guys! Let's dive into a fun math problem. This is a classic riddle-style question. We're going to figure out how many apples Mahmud has. It's a cool way to use logic and a bit of math to solve a real-world-ish problem. So, buckle up, and let's get started! We need to use our knowledge to understand the concept and find the solution. This is a great exercise to improve your problem-solving skills. Let's start by breaking down the information given and setting up the problem clearly. Then we'll go step by step, making sure we understand each part, and finally, we'll arrive at the answer. Alright, enough chat, let's crunch some numbers and find out exactly how many apples Mahmud has! We will use logical reasoning and some simple arithmetic to find the solution. This will make you think critically. This kind of problem is a great mental exercise, helping you sharpen your ability to think and solve puzzles. Are you ready? I think you are, so let us start.

Understanding the Problem

Okay, the problem says: "Mahmud has fewer than 20 apples." That's our first piece of information. It tells us the upper limit, right? He doesn't have more than 20 apples. Next, we're given two scenarios about how Mahmud tries to arrange his apples. The problem presents us with a couple of different apple-arranging scenarios. The first scenario involves Mahmud putting his apples into groups of three. When he does this, he has some apples left over. The second scenario is where he puts his apples into groups of five. However, this time, he falls short by two apples. It says, "If he puts them on plates of 3, he has 1 apple left over." and "If he puts them on plates of 5, he's 2 apples short." That's the essence of the question. We know that Mahmud has less than twenty apples, and we have two different scenarios about how he organizes them. These scenarios will help us find the right answer. These clues give us enough to determine the exact number of apples Mahmud has. Understanding these two conditions is key to solving the problem.

Let's translate these clues into mathematical terms. We can think of it like this. The number of apples, let's call it 'x', is less than 20. When 'x' is divided by 3, the remainder is 1. And when 'x' is divided by 5, the remainder is -2 (or, in other words, 3 when we're looking at remainders since a shortage of 2 is the same as having 3 remaining when grouped by 5). This is a great opportunity to refresh your understanding of remainders and basic division. We will use this information to narrow down the possibilities. These remainders are super important because they give us a constraint for the number of apples. The goal is to find a number that satisfies both conditions. So, the core of the problem revolves around understanding remainders and working with them. By using this information, we can begin to find the answer.

Solving the Puzzle

Now comes the fun part: solving the puzzle! We know Mahmud has fewer than 20 apples. Let's make a list of the possible numbers of apples he could have, from 1 to 19. Then we'll check each one against the conditions given in the problem. We know that if Mahmud tries to arrange his apples in groups of three, he'll have one left over. So, let's test the possible numbers. We're going to go through each number and determine if it fits the conditions. Let's start testing!

  • 1: 1 divided by 3 leaves a remainder of 1. But, 1 divided by 5 leaves a remainder of 1, and we need a remainder of -2 (or 3). So, 1 is not a solution.
  • 2: 2 divided by 3 leaves a remainder of 2. Nope.
  • 3: 3 divided by 3 leaves a remainder of 0. Nope.
  • 4: 4 divided by 3 leaves a remainder of 1. Okay, this satisfies the first condition! 4 divided by 5 leaves a remainder of 4. Nope.
  • 5: 5 divided by 3 leaves a remainder of 2. Nope.
  • 6: 6 divided by 3 leaves a remainder of 0. Nope.
  • 7: 7 divided by 3 leaves a remainder of 1. This satisfies the first condition! 7 divided by 5 leaves a remainder of 2. Nope.
  • 8: 8 divided by 3 leaves a remainder of 2. Nope.
  • 9: 9 divided by 3 leaves a remainder of 0. Nope.
  • 10: 10 divided by 3 leaves a remainder of 1. This satisfies the first condition! 10 divided by 5 leaves a remainder of 0. Nope.
  • 11: 11 divided by 3 leaves a remainder of 2. Nope.
  • 12: 12 divided by 3 leaves a remainder of 0. Nope.
  • 13: 13 divided by 3 leaves a remainder of 1. This satisfies the first condition! 13 divided by 5 leaves a remainder of 3. Bingo!
  • 14: 14 divided by 3 leaves a remainder of 2. Nope.
  • 15: 15 divided by 3 leaves a remainder of 0. Nope.
  • 16: 16 divided by 3 leaves a remainder of 1. This satisfies the first condition! 16 divided by 5 leaves a remainder of 1. Nope.
  • 17: 17 divided by 3 leaves a remainder of 2. Nope.
  • 18: 18 divided by 3 leaves a remainder of 0. Nope.
  • 19: 19 divided by 3 leaves a remainder of 1. This satisfies the first condition! 19 divided by 5 leaves a remainder of 4. Nope.

We went through all the possibilities, and the number 13 fits the description. It's less than 20. When divided by 3, it leaves a remainder of 1. And when divided by 5, it leaves a remainder of 3 (or -2, which means it's 2 short). Therefore, Mahmud has 13 apples.

Conclusion

Congratulations, guys! We've successfully solved the puzzle and figured out how many apples Mahmud has. We started by understanding the problem, broke down the conditions, and then systematically checked the possibilities until we found the answer. This was a fun way to use math and logic together. Hopefully, you enjoyed this brain teaser. Remember, the key is to break down the problem into smaller parts, think logically, and test your assumptions. Keep practicing, and you'll become a problem-solving pro in no time. See ya!