Solving the Hen and Egg Puzzle: A Comprehensive Guide

Many have debated the classic riddle, 'If a hen and a half lay an egg and a half in two days and a half, how many eggs will half a dozen hens lay in half a dozen days?'

Breaking Down the Problem

This riddle is a fun and engaging way to explore basic mathematical concepts and problem-solving skills. Let's break it down step by step to find the solution.

Step 1: Determine the Rate of Egg-Laying for One Hen

First, let's determine how many eggs one hen can lay in a specific time frame:

Given that 1.5 hens lay 1.5 eggs in 2.5 days, we can find the rate for one hen.

Rate of one hen ( frac{1.5 text{ eggs}}{1.5 text{ hens}} 1 text{ egg in 2.5 days} )

Next, we calculate the rate for one hen per day:

Rate per day ( frac{1 text{ egg}}{2.5 text{ days}} 0.4 text{ eggs per day} )

Step 2: Determine the Egg-Laying Capacity of Six Hens in One Day

Now that we have the rate for one hen, we can calculate the number of eggs six hens will lay in one day:

Eggs by 6 hens in one day 6 times 0.4 2.4 text{ eggs per day} )

Step 3: Determine the Total Number of Eggs Laid by Six Hens in Six Days

To find the total number of eggs laid by six hens in six days, follow these steps:

Total eggs in 6 days 2.4 text{ eggs/day} times 6 text{ days} 14.4 text{ eggs} )

Therefore, half a dozen hens (which is six hens) will lay 14.4 eggs in half a dozen days (six days).

Solving the Related Riddle

Let's now tackle another variation of the riddle: 'If a hen and a half lay an egg and a half in a day and a half, how many eggs will half a dozen hens lay in half a dozen days?'

Step 1: Determine the Rate of Egg-Laying for One Hen in This Version

Starting from the given information:

3 hens lay 3 eggs in 2.5 days. Rate of one hen ( frac{3 text{ eggs}}{3 text{ hens}} 1 text{ egg in 2.5 days} ) Rate per day ( frac{1 text{ egg}}{2.5 text{ days}} 0.4 text{ eggs per day} )

Step 2: Determine the Egg-Laying Capacity of Six Hens in One Day

Using the rate per day, we can calculate the number of eggs six hens will lay in one day:

Eggs by 6 hens in one day 6 times 0.4 2.4 text{ eggs per day} )

Step 3: Determine the Total Number of Eggs Laid by Six Hens in Six Days

Finally, we calculate the total number of eggs laid by six hens in six days:

Total eggs in 6 days 2.4 text{ eggs/day} times 6 text{ days} 14.4 text{ eggs} )

Therefore, half a dozen hens will lay 14.4 eggs in half a dozen days.

Note: In practical terms, this riddle is designed to test your understanding of rates and proportions, and the solution is mathematically precise.

Conclusion

The riddles discussed here not only provide a fun challenge but also help in sharpening problem-solving skills. Understanding the rate of egg-laying and applying it to different scenarios can be quite illuminating. These riddles can be a great way to engage in family discussions or team problem-solving activities.

If you found this useful, check out more similar riddles and math puzzles on YouTube, where experts break down solving such puzzles in a step-by-step manner. Happy solving!