Difference between revisions of "2021 JMPSC Sprint Problems/Problem 5"

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==Solution==
 
==Solution==
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There exists a <math>2</math> digit even number that has digits that sum to <math>17</math>. Pertaining to the assumption that this operation is in base <math>10</math>, there exists only <math>10</math> digits to be used, specifically only <math>5</math> for the first digit. Only <math>8</math> and <math>9</math> may be used, as there isn't other pair of digits which sum to <math>17</math>
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The only two numbers in which satisfy the fact that the digits sum to <math>17</math> are <math>98</math> and <math>89</math>. Yet, only <math>98</math> works because it is the only one in which satisfies the condition that the number must be even.
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Therefore, <math>\boxed{98}</math> is the only two-digit even number that has digits that sum to <math>17</math>.
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-OofPirate

Revision as of 00:55, 11 July 2021

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

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