Solve Weedy Willie's Division Puzzle

In summary, the conversation discusses a puzzle about a farmer, Weedy Willie, who needs to divide his cornfield between himself and his four sons in proportion to their work rates. The solution involves dividing the field into a two-digit square number of parts and giving each son a certain number of parts. After considering various conditions and employing mathematical techniques, the solution is found to be that the field was divided into 49 equal parts, with each son receiving 13 parts and Weedy receiving 9 parts. However, there may be some discrepancies with the solution provided in a puzzle periodical. The conversation also mentions a book, "Mathematical Puzzles and Curiosities" by Barry R Clarke, which contains similar puzzles.
  • #1
K Sengupta
113
0
A couple of years back, I came across a nice problem in a puzzle magazine.

PROBLEM:

Weedy Willie was getting too old to work the land alone so he decided to divide his cornfield between himself and his four sons in proportion to their five work rates. He knew that Rastus, Wig, Twig and Swig together could plant a field of corn in five hours whereas Wig, Twig and Swig and himself together could manage the same task in six hours. So Weedy divided his field into a two-digit square number of parts and kept just one part for himself. Now, Wig, Twig and Swig were identical triplets so each received the same whole number of parts. How many parts did each son get?

( Methodology:

Let the total number of parts dividing the field be p^2; 1<=p<=9. Let the fraction of the field received by each of the triplets, Rastus and Weedy be a/p^2, b/p^2 and 1/p^2 respectively.
Then, 3a+b+1 = p^2...(i)
Let the total number of hours taken by each of the triplets, Rastus and Weedy be x, y and z.
Then the proportion of land received by each of the triplets, Rastus and Weedy are in the proportion
1/x : 1/y: 1/z ...(ii)
Comparing (i) and (ii): x = z/a; y = z/b

Now, the fraction of the work finished by each of the Triplets, Rastus and Weedy separately in 1 hour are 1/x, 1/y and 1/z.

So, by conditions of the problem

3/x + 1/z = 1/6; 3/x + 1/y = 1/5
Or, (3a+1)/z=1/6; (3a+b)/z = 1/5
Or, (b-1)/z = 1/5 - 1/6 = 1/30; giving, b = z/30 + 1
But (3a+1)/z = 1/6; (3a+b)/z = 1/5 and 3a+b+1 = p^2 yields:
a = (5*p^2 - 11)/18; b = (p^2 + 5)/6
Since a and b must be positive integers; it follows that both (5*p^2 -11)/18 and (p^2+5)/6 must be integers.

Employing either number theoretic techniques or by trial and error, p is 7 in the interval 1<=p<=9.
This gives (a,b) = (13,9)

Hence, the field was divided into 49 equal parts. The # parts received by each of the triplets (Wig, Twig, Swig) = (13,13,13) and the # parts received by Rastus is 9.(NOTE:
However, in terms of the solution provided in the said puzzle periodical:

The field was divided into 16 equal parts. The # parts received by the triplets (Wig, Twig, Swig) = (3,3,3) and the # parts received by Rastus is 6.

In terms of the methodology given above, this would appear to contravene the tenets corresponding to the problem; since:
for p=4; (p^2 + 5)/6 = 3.5, which is not an integer.)

Consequently, I solicit comments from the members on the foregoing matter.
 
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  • #2

Related to Solve Weedy Willie's Division Puzzle

1. How do you solve Weedy Willie's Division Puzzle?

To solve Weedy Willie's Division Puzzle, you must first understand the rules of the puzzle. You will start with a number, and you must divide that number by a given divisor. The resulting quotient will then be divided by another given divisor, and so on until you reach the final divisor. The goal is to end up with a final remainder of 0.

2. What happens if you don't end up with a remainder of 0?

If you don't end up with a remainder of 0, then you have not successfully solved Weedy Willie's Division Puzzle. You may have made a mistake in your calculations or may have used the wrong divisors. You can try again or check your work to find where you went wrong.

3. Can you use any divisors to solve the puzzle?

No, there are specific divisors that must be used in order to solve Weedy Willie's Division Puzzle. These divisors are provided in the puzzle and must be used in the given order. Using different divisors or changing the order will result in an incorrect solution.

4. How long does it take to solve Weedy Willie's Division Puzzle?

The time it takes to solve Weedy Willie's Division Puzzle will vary depending on the complexity of the puzzle. Some puzzles may be relatively easy and can be solved quickly, while others may require more time and effort. It also depends on the individual's math skills and ability to solve division problems.

5. Is there a trick to solving Weedy Willie's Division Puzzle?

There is no specific trick to solving Weedy Willie's Division Puzzle. It requires basic division skills and careful calculations. Some people may find certain strategies or methods to be helpful, but ultimately it comes down to following the rules and making accurate calculations.

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