Summed exponents for a 8- digit positive decimal integer

AI Thread Summary
The discussion centers around the cryptarithmetic equation involving the 8-digit integer ABCDEFGF, where each letter represents a unique decimal digit from 0 to 9, excluding the digits 1 and 9. The structure of the number requires that nonzero even digits appear in ascending order, while odd digits must be arranged in descending order. Additionally, neither A nor E can be zero. The equation presented is ABCDEFGF = AE + BE + CE + DE + EE + FE + GE + FE, which adds complexity to finding potential solutions. Participants express difficulty in solving the equation, indicating that it presents a significant challenge.
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
 
Physics 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
 

Thread 'Predictions for the Nobel Prize in Physics 2025'

Similar to the 2024 thread, here I start the 2025 thread. As always it is getting increasingly difficult to predict, so I will make a list based on other article predictions. You can also leave your prediction here. Here are the predictions of 2024 that did not make it: Peter Shor, David Deutsch and all the rest of the quantum computing community (various sources) Pablo Jarrillo Herrero, Allan McDonald and Rafi Bistritzer for magic angle in twisted graphene (various sources) Christoph...
View full post »
Thread 'My experience as a hostage'

Thread 'My experience as a hostage'

I believe it was the summer of 2001 that I made a trip to Peru for my work. I was a private contractor doing automation engineering and programming for various companies, including Frito Lay. Frito had purchased a snack food plant near Lima, Peru, and sent me down to oversee the upgrades to the systems and the startup. Peru was still suffering the ills of a recent civil war and I knew it was dicey, but the money was too good to pass up. It was a long trip to Lima; about 14 hours of airtime...
View full post »

Similar threads

MHB A positive integer divisible by 2019 the sum of whose decimal digits is 2019.
Replies
2
Views
2K
Divide by one digit numbers by two digit numbers, and add to get 1
Replies
4
Views
6K
Some Summed Digits In A 9-Digit Positive Integer
Replies
2
Views
4K
Decimal integers with nonzero digits and sum of powers puzzle
Replies
7
Views
4K
MHB Representation of signed integers of base B
Replies
17
Views
1K
Two successive digits and divisibility puzzle
Replies
1
Views
3K
Seven digit base eight positive integer puzzle
Replies
2
Views
3K
Show That If Alt Sum of Digits Div By 11, n Is Divisible By 11
Replies
1
Views
2K
8-digit number and divisibility puzzle
Replies
3
Views
8K
Pascal - absolute sum of digits
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top