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,
is 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
, then
This doesn't work because
isn't divisible by
. If
, then
Therefore,
. 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
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