Summed exponents for a 8- digit positive decimal integer

Click For Summary
SUMMARY

The discussion centers on the cryptarithmetic equation involving the 8-digit integer ABCDEFGF, where each letter represents a unique decimal digit from 0 to 9, excluding 1 and 9. The even digits must be arranged in ascending order, while the odd digits are in descending order. The equation is defined as ABCDEFGF = AE + BE + CE + DE + EE + FE + GE + FE, presenting a challenge in finding valid solutions given the constraints on digit placement and values.

PREREQUISITES
  • Understanding of cryptarithmetic puzzles
  • Familiarity with integer properties and digit constraints
  • Basic knowledge of combinatorial mathematics
  • Experience with logical reasoning and problem-solving techniques
NEXT STEPS
  • Explore techniques for solving cryptarithmetic equations
  • Research combinatorial optimization methods
  • Learn about digit representation and constraints in mathematical puzzles
  • Investigate programming approaches for automating cryptarithmetic solutions
USEFUL FOR

Mathematicians, puzzle enthusiasts, educators, and anyone interested in solving complex cryptarithmetic equations.

K Sengupta
Messages
113
Reaction score
0
ABCDEFGF is an 8-digit positive decimal integer, where each letter represents a different decimal digit from 0 to 9. The digits 1 and 9 do not appear. The nonzero even digits appear in ascending order, and the odd digits appear in descending order in ABCDEFGF. None of A and E can be zero.

What are the possible solution(s) to this cryptarithmetic equation?

ABCDEFGF = AE + BE + CE + DE + EE + FE + GE + FE
 
Mathematics news on Phys.org
Oh no!
I have been looking the page off-line as archive where the equation was read as:
ABCDEFGF = AE + BE + CE + DE + EE + FE + GE + FE

Seems difficult
 
A=2 B=4 C=6 D=7 E=8 F=0 G=5

DaveE
 

Similar threads

MHB A positive integer divisible by 2019 the sum of whose decimal digits is 2019.
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Divide by one digit numbers by two digit numbers, and add to get 1
  • · Replies 4 ·
Replies
4
Views
6K
Undergrad Some Summed Digits In A 9-Digit Positive Integer
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Decimal integers with nonzero digits and sum of powers puzzle
  • · Replies 7 ·
Replies
7
Views
4K
MHB Representation of signed integers of base B
  • · Replies 17 ·
Replies
17
Views
2K
Challenge Math Challenge - April 2021
  • · Replies 102 ·
4
Replies
102
Views
11K
Mathematica This Week's Finds in Mathematical Physics (Week 228)
  • · Replies 2 ·
Replies
2
Views
3K
Schools How well does this course prepare me for college math?
  • · Replies 10 ·
Replies
10
Views
5K
Mathematica This Week's Finds in Mathematical Physics (Week 228)
  • · Replies 2 ·
Replies
2
Views
4K