text: # Difference between revisions of "2021 JMPSC Sprint Problems/Problem 5"
  
  ## Problem
  
  What two-digit even number has digits that sum to $17$?
  
  ## Solution
  
  There exists a $2$ digit even number that has digits that sum to $17$. Pertaining to the assumption that this operation is in base $10$, there exists only $10$ digits to be used, specifically only $5$ for the first digit. Only $8$ and $9$ may be used, as there isn't other pair of digits which sum to $17$
  
  The only two numbers in which satisfy the fact that the digits sum to $17$ are $98$ and $89$. Yet, only $98$ works because it is the only one in which satisfies the condition that the number must be even.
  
  Therefore, $\boxed{98}$ is the only two-digit even number that has digits that sum to $17$.
  
  -OofPirate
  
  ## Solution 2
  
  The number must have digits $8$ and $9$. $89$ is odd but $\boxed{98}$ is even.
  
  - kante314 -