Difference between revisions of "2021 WSMO Team Round Problems/Problem 2"
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==Problem== | ==Problem== | ||
Bobby has some pencils. When he tries to split them into 5 equal groups, he has 2 left over. When he tries to split them into groups of 8, he has 6 left over. What is the second smallest number of pencils that Bobby could have? | Bobby has some pencils. When he tries to split them into 5 equal groups, he has 2 left over. When he tries to split them into groups of 8, he has 6 left over. What is the second smallest number of pencils that Bobby could have? | ||
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| + | ''Proposed by pinkpig'' | ||
==Solution== | ==Solution== | ||
| + | We want <math>x \equiv 2 \pmod{5}</math> and <math>x \equiv 6 \pmod{8}</math>. The smallest such <math>x</math> is <math>22</math>, and the next is <math>62</math>. So, our answer is <cmath>\boxed{62}.</cmath> | ||
| + | ~pinkpig | ||
Latest revision as of 13:06, 9 September 2025
Problem
Bobby has some pencils. When he tries to split them into 5 equal groups, he has 2 left over. When he tries to split them into groups of 8, he has 6 left over. What is the second smallest number of pencils that Bobby could have?
Proposed by pinkpig
Solution
We want 
and 
. The smallest such 
is 
, and the next is 
. So, our answer is ![\[\boxed{62}.\]](http://latex.artofproblemsolving.com/b/d/3/bd3411f2a28f92fe1f73ccb0e8c2b36d8799eae1.png)
~pinkpig
