2021 JMPSC Accuracy Problems/Problem 7
Problem
If , , and each represent a single digit and they satisfy the equation find .
Solution
Notice that can only be , , and . However, and are not divisible by , so Thus,
~Bradygho
Solution 2
Clearly we see does not work, but works with simple guess-and-check. We have , so and . The answer is
~Geometry285
Solution 3
Easily, we can see that . Therefore,We can see that must be or . If , thenThis doesn't work because isn't divisible by . If , thenTherefore, . So, we have .
- kante314 -
Solution 4
Notice that the only values of that have for some are and . If , then we have , and so . Notice that is not divisible by , so is not a valid solution. Next, when , we have that . Solving for and tells us that and , so the answer is .
~Mathdreams
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.