MHB Solving for $k$: Digit Product = $\dfrac{25k}{8}-211$

  • Thread starter Thread starter anemone
  • Start date Start date
  • Tags Tags
    Product
Click For Summary
The discussion focuses on finding positive integers \( k \) such that the product of the digits of \( k \) equals \( \frac{25k}{8} - 211 \). Participants confirm that both 72 and 88 satisfy this equation. There is a suggestion to share the solution with MHB for further insights. The conversation emphasizes the importance of verifying the conditions for \( k \) to ensure all solutions are identified. Overall, the thread highlights a mathematical exploration of digit products in relation to a linear equation.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Find all positive integers $k$ such that the product of the digits of $k$, in the decimal system, equals $\dfrac{25k}{8}-211$.
 
Mathematics news on Phys.org
72 and 88
 
Yes, your answer is correct. Do you think you can share with MHB of your solution?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Recreational Number Theory, Unsolved Problem
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
MHB What are the values of n and k in n+8=2^k when n!+8 = 2^k?
  • · Replies 8 ·
Replies
8
Views
2K
High School Proof of Chain Rule: Understanding the Limits
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find the amount of sand in each bag
  • · Replies 1 ·
Replies
1
Views
1K
MHB Solving Integer Equations with $a$ and $b$
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
MHB Value of $\dfrac{2k^2}{k-1}$: Solving the Equation
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solving Permutations Question with Restrictions
  • · Replies 3 ·
Replies
3
Views
1K
MHB A positive integer divisible by 2019 the sum of whose decimal digits is 2019.
  • · Replies 2 ·
Replies
2
Views
2K