Product equality and sum of squares equality puzzle

Click For Summary
The discussion revolves around solving a cryptarithmetic puzzle where each letter represents a unique digit from 0 to 9, with no leading zeros allowed. The main equation to solve is ABCD multiplied by EF equals GHJB multiplied by KE. Additionally, the relationship (EH)² + (KC)² = (KH)² must also hold true. Participants are tasked with finding the correct digit substitutions that satisfy both equations simultaneously. The challenge lies in ensuring that all letters correspond to different digits while adhering to the mathematical constraints.
K Sengupta
Messages
113
Reaction score
0
Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero.

ABCD*EF=GHJB*KE, and:

(EH)2 + (KC)2 = (KH)2
 
Physics news on Phys.org
abcd*ef=ghjb*ke
9807*14=6538*21

(eh)2 + (kc)2 = (kh)2
(15)2 + (20)2 = (25)2
 

Similar threads

Sum, difference and equality puzzle
  • · Replies 2 ·
Replies
2
Views
3K
(4-digit number)*(6-digit number) equals a factorial
  • · Replies 1 ·
Replies
1
Views
4K
Sum the squares cryptarithmetically, get square
  • · Replies 5 ·
Replies
5
Views
2K
How Can You Solve the 3x3 Square and Common Sum Puzzle?
  • · Replies 1 ·
Replies
1
Views
5K
Multiplying six by two gets twelve
  • · Replies 1 ·
Replies
1
Views
3K
Squares, subsquares and arrangement puzzle
  • · Replies 2 ·
Replies
2
Views
3K
Two successive digits and divisibility puzzle
  • · Replies 1 ·
Replies
1
Views
3K
Pan suspended by a spring (Energy + SHM)
  • · Replies 20 ·
Replies
20
Views
4K
Getting the multiplier, multiplicand and the product with U’s
  • · Replies 2 ·
Replies
2
Views
4K
Decimal integers with nonzero digits and sum of powers puzzle
  • · Replies 7 ·
Replies
7
Views
4K