Today, we’re diving into a puzzle that might just make you do a double-take! The setup is deceptively simple, but don’t let that fool you. The challenge is to determine the father’s age based on the following clues:

1. The father’s age is a two-digit number made up of two consecutive digits that also represent his two sons’ ages.
2. The sum of all three ages adds up to 51.

Ready to put your logical thinking to the test? Let’s break down this puzzle step-by-step and find out how old the father is!

Common Pitfalls People Encounter

Before we start solving, let’s look at a few common mistakes people make when tackling this puzzle:

• Misinterpreting “Consecutive Figures”: Many people read “two consecutive figures” and assume it means two sequential numbers, like 34 and 35, instead of a single two-digit number composed of consecutive digits, such as 39.
• Ignoring the Sum of Ages: The puzzle requires that the sum of all three ages equals 51. It’s easy to overlook this detail, but it’s crucial for finding the correct solution.
• Overcomplicating the Solution: Some people tend to jump into complex equations or guess random numbers, when a systematic, logical approach is all that’s needed to solve the puzzle.

Now that we’re aware of these common mistakes, let’s break down the solution methodically.

Step-by-Step Solution to the Puzzle

Step 1: Define the Variables

Let’s assign variables to the ages:

• Let’s say the father’s age is represented by aaa.
• Since the father’s age is a two-digit number made of his sons’ ages, we’ll define these ages as bbb and ccc, where bbb and ccc are consecutive digits.
• We can then express the father’s age, aaa, as a=10b+ca = 10b + ca=10b+c since aaa is a two-digit number with bbb as the tens digit and ccc as the units digit.

Step 2: Set Up the Equation Based on the Sum of Ages

According to the puzzle, the sum of the father’s age and his two sons’ ages is 51. This gives us the equation:

a+b+c=51

Now, we substitute aaa from our earlier expression: 10b+c+b+c=51

Combine like terms: 11b+2c=51

Step 3: Solve for Possible Values of bbb and ccc

To find values for bbb and ccc, we’ll isolate ccc: 2c=51−11b2c

c = (51 – 11b)/2

Since bbb and ccc are consecutive integers, bbb must be a single-digit number (0 through 9), and we need ccc to be a whole number. Let’s try possible values for bbb to see which results in ccc as an integer.

Testing Values for bbb:

1. Try b=3: c=(51−11×3)/2
   c=(51−33)/2
   c=18/2
   c=9
2. Here, b=3 and c=9, which works! This makes the father’s age
   a=10b+c=10×3+9=39
3. Check the Sum:
   Now, let’s confirm that the ages satisfy the sum of 51:
   39+3+9=51
   Perfect! This means our solution holds true. The father is 39 years old, and his two sons are 3 and 9.

Solution Recap

To summarize:

• We determined that the father’s age, 39, is formed by two consecutive digits, 3 and 9, representing the ages of his two sons.
• By carefully interpreting the clues and using simple algebra, we confirmed that the sum of all three ages equals 51.

Why This Puzzle Works as a Great Brain Exercise

This puzzle is an excellent test of logic and attention to detail. It requires you to interpret clues carefully, avoid assumptions, and apply basic algebra in a structured way. Puzzles like this challenge us to think critically and ensure each step logically follows the previous one.

Encouragement to Share the Puzzle with Friends

Did you figure out the answer, or did it take a few tries? Share this puzzle with friends or family and see how they approach it! It’s always interesting to see different problem-solving methods, and discussing the solution is a great way to bond over a bit of mental exercise.

These types of puzzles are fantastic for improving our logical reasoning and keeping our minds sharp. So, next time you come across a riddle or a brain teaser, dive right in, and don’t be afraid to challenge yourself. Enjoy the process, stay curious, and most importantly, have fun!