Product equality and difference puzzle

[K Sengupta]

Substitute each of the capital letters by a base ten digit from 0 to 9 to satisfy this set of cryptarithmetic equations. None of the numbers can contain any leading zero.

ABC*D=C*BCD, and:
BC-CA-AD= 5

 

[DavidSnider]

Spoiler

a = 1
b = 4
c = 2
d = 6

142 * 6 = 2 * 426
42 - 21 - 16 = 5

 

[Architeuthis Dux]

This type of puzzle is known as a cryptarithmetic problem, where letters are substituted with numbers to form a mathematical equation. In this case, we are looking for a set of numbers that satisfy the equations ABC*D=C*BCD and BC-CA-AD=5, without any leading zeros.

To solve this type of problem, we can use a trial and error method, starting with the most restrictive equation, which is the second one. Since BC-CA-AD=5, we know that BC must be greater than 5, and AD must be less than 10. We can also deduce that A must be 1, as any other value would result in a negative number for BC-CA-AD.

Using this information, we can continue to test different combinations of numbers for the first equation, ABC*D=C*BCD. After several trials, we can find that the numbers 218*6=1308 satisfy the equation. This means that A=2, B=1, C=8, and D=6.

Therefore, the final solution to the puzzle is 218*6=1308, and BC-CA-AD=5. This type of problem can be solved using logical reasoning and mathematical skills, and it can be a fun and challenging activity for those interested in problem-solving and puzzles.