Difference between revisions of "2021 JMPSC Sprint Problems/Problem 5"
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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 
?
Solution
There exists a 
digit even number that has digits that sum to . Pertaining to the assumption that this operation is in base 
, there exists only digits to be used, specifically only 
for the first digit. Only 
and 
may be used, as there isn't other pair of digits which sum to
The only two numbers in which satisfy the fact that the digits sum to are 
and 
. Yet, only works because it is the only one in which satisfies the condition that the number must be even.
Therefore, 
is the only two-digit even number that has digits that sum to .
-OofPirate
