Today, we’re diving into a mind-bending puzzle that’s sure to make you scratch your head! The challenge is simple but tricky: A father’s age is a two-digit number formed by two consecutive figures—the ages of his two sons. The total of all three ages equals 51. How old is the father?
Puzzles like this one may seem straightforward, but it’s the little details that can often trip you up. Are you ready to put your logic skills to the test? Let’s break down the steps to solve this puzzle and find out how old the father is!
Common Pitfalls and Why They Happen
When tackling this puzzle, many people make common mistakes that lead them to incorrect answers. These mistakes typically arise from a lack of attention to detail or from not fully understanding how the puzzle’s clues interrelate. Here are a few examples:
- Misinterpreting the “Consecutive Figures” Clue: Some might interpret consecutive figures as two numbers that follow each other, like 34 and 35, rather than a single two-digit number where the digits themselves are consecutive, like 39.
- Ignoring the Total Sum Requirement: It’s easy to get fixated on finding the father’s age and overlook the requirement that the sum of all three ages must be 51. This clue is essential to solving the puzzle correctly.
- Overthinking the Problem: Often, people try complex algebra or guess at random numbers, when a more straightforward logical approach is all that’s needed. By breaking it down step-by-step, you can avoid overcomplicating things.
Let’s look at how to solve this puzzle systematically, using each clue provided.
Step-by-Step Solution
We’ll go through the puzzle step-by-step and pay close attention to each piece of information given. Let’s start by breaking down what we know and using basic algebra to solve the puzzle.
Step 1: Define the Variables
Let’s assign some variables to the father’s age and the sons’ ages:
- Let’s call the father’s age a, and the ages of his two sons b and c.
- According to the puzzle, the father’s age is a two-digit number, where a consists of two consecutive digits, b and c.
Thus, we can express a as follows: a=10b+c
Step 2: Sum of the Ages
We’re given that the sum of all three ages equals 51. This gives us the equation: a+b+c=51
Now, we substitute the value of a from our first equation into this sum equation: 10b+c+b+c=51
Simplify by combining like terms: 11b+2c=51
Step 3: Solve for Possible Values
Now, let’s isolate c to find possible values for both b and c. Rearranging the equation:
2c=51−11b
c = (51 – 11b)/2
At this point, we can try values of b to ensure c is a valid integer (since age is always a whole number). Let’s plug in values for b and check if c also results in a whole number.
Trying b = 3
c=(51−11×3)/2
c=(51−33)/2
c=18/2=9
Here, we have b = 3 and c = 9, which works!
This gives us:
- Father’s age a=10×3+9=39
- The two sons’ ages are 3 and 9.
Now, let’s check if these satisfy the sum:39+3+9=51
The total equals 51, which confirms our solution. The father is 39 years old.
Solution Recap
To sum up, we found that the father is 39 years old, with his sons being 3 and 9 years old. By carefully using the clues and applying simple algebra, we’ve solved the puzzle accurately. The critical detail was interpreting the father’s age as a two-digit number formed by two consecutive digits.
Final Thoughts and Call to Action
Puzzles like this one are not only fun but also excellent exercises for logical thinking. They encourage us to look closely at details, think methodically, and avoid jumping to conclusions. Now that you’ve worked through this puzzle, try sharing it with friends or family to see if they can solve it too!
What was your thought process when you first attempted the puzzle? Did you approach it differently, or did you come up with the same answer? Comment below with your solution and let’s see if anyone has an alternative approach! And if you enjoyed this puzzle, keep challenging yourself with more riddles and logic games to sharpen your problem-solving skills.
