Fun Math Puzzle: How Many Coins in the Piggy Bank?

Create a Python program to solve the following puzzle:

Each year, a baby receives a number of coins in their piggy bank equal to their age in years. Determine which birthday the baby is celebrating if there are 21 coins in the piggy bank.

Fun Math Puzzle: How Many Coins in the Piggy Bank?

To solve this puzzle, we need to find out which birthday the baby celebrates when the total number of coins in the piggy bank is 21.

This puzzle can be formulated mathematically where each year the baby gets coins equal to their age.

The sum of the first ( n ) natural numbers can be calculated using the formula:

S = n * (n + 1) / 2

Given ( S = 21 ), we need to find ( n ) such that:

n * (n + 1) / 2 = 21

We will write a Python program to solve this by iterating through possible values of ( n ) and checking when the sum matches 21.

🧩 So, The Answer is 6 🧩

Here’s the plan in pseudocode for “How Many Coins in the Piggy Bank”:

Initialize a variable total_coins to 21.
Iterate over possible ages starting from 1.
Calculate the sum of coins for each age using the formula for the sum of the first ( n ) natural numbers.
Check if the calculated sum matches total_coins.
If a match is found, print the age.

Here is the Python code that implements this logic:

def find_birthday(total_coins):
    age = 1
    while True:
        sum_coins = age * (age + 1) // 2  # Sum of the first 'age' natural numbers
        if sum_coins == total_coins:
            return age
        age += 1

total_coins = 21
birthday = find_birthday(total_coins)
print(f"The baby celebrates their {birthday}th birthday.")

This program iterates through each possible age, calculates the total number of coins, and checks if it matches the given number of coins (21). When it finds a match, it prints the age.

We can rewrite the code using a for loop to determine the birthday based on the total number of coins. Here’s how you can do it:

def find_birthday(total_coins):
    for age in range(1, total_coins + 1):
        sum_coins = age * (age + 1) // 2  # Sum of the first 'age' natural numbers
        if sum_coins == total_coins:
            return age

total_coins = 21
birthday = find_birthday(total_coins)
print(f"The baby celebrates their {birthday}th birthday.")

In this version, the for loop iterates over each possible age from 1 up to the total number of coins. It calculates the sum of coins for each age and checks if it matches the given total. If a match is found, it returns the age.

Suggestions for next steps:

a. Run the provided Python code to verify that it correctly calculates the birthday.

b. Add a function to validate the result by comparing it with the mathematical approach.

Illustration Description:

The illustration depicts a baby with a piggy bank, celebrating their birthday each year. Each year is represented by a series of stacked coins, symbolizing the number of coins the baby receives corresponding to their age.

Baby and Piggy Bank:
- The baby is holding a colorful piggy bank.
- The baby is wearing a birthday hat to signify the celebration.
Coins for Each Year:
- Next to the baby, there is a sequence of stacks of coins.
- Each stack has a label indicating the baby’s age for that year.
- For example, the first stack has 1 coin, the second stack has 2 coins, the third stack has 3 coins, and so on.
- The total number of coins across all stacks is highlighted to be 21.
Visual Summary:
- There is a large “21 Coins” banner to emphasize the total.
- An arrow points from the total coin count to the final stack, indicating that we need to determine the corresponding age.
Mathematical Representation:
- At the bottom of the illustration, a simple mathematical formula:
  Sum = n * (n + 1) / 2
- This represents the sum of coins formula used to solve the puzzle.
Solution Highlight:
- The illustration concludes with the age (6 years old) highlighted, indicating that the baby is celebrating their 6th birthday when there are 21 coins in the piggy bank.

🧩 Puzzle Time! 🧩

Here’s a fun challenge for all you math enthusiasts and parents out there! 🎉👶

Puzzle: Each year, a baby receives a number of coins in their piggy bank equal to their age in years. If there are 21 coins in the piggy bank, what birthday is the baby celebrating? 🤔💭

🔢 Hint: Think about the sum of the first ‘n’ natural numbers! 🔢

Feeling up for the challenge? Share your answers and thoughts in the comments below! ⬇️ Let’s see who can crack it first! 🏅

Puzzle #MathChallenge #BrainTeaser #FunWithNumbers #ParentalFun #SmartKids #ChallengeAccepted

Here’s the metadata for the blog post:

title: "Fun Math Puzzle: How Many Coins in the Piggy Bank?"
description: "Join us for a fun math puzzle! Determine which birthday a baby is celebrating if they have 21 coins in their piggy bank. Perfect for math enthusiasts and parents alike!"
author: "Vitaly Oustinov"
date: "2024-07-05"
category: "Puzzles"
tags: ["math", "puzzle", "brain teaser", "parenting", "fun", "education"]
image: "https://daily-on.com/wp-content/uploads/2024/07/20240705-1-A-cheerful-baby-with-a-piggy-bank-surrounded-by-coin-stacks-and-a-festive-birthday-atmosphere.-No-banknotes.png"
keywords: ["math puzzle", "brain teaser", "sum of natural numbers", "parenting fun", "educational puzzle"]