https://artofproblemsolving.com/wiki/index.php?title=2020_CIME_I_Problems/Problem_15&feed=atom&action=history2020 CIME I Problems/Problem 15 - Revision history2024-03-28T23:44:38ZRevision history for this page on the wikiMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=2020_CIME_I_Problems/Problem_15&diff=132940&oldid=prevJbala: Created page with "==Problem 15== Find the number of integer sequences <math>a_1, a_2, \ldots, a_6</math> such that :(1) <math>0 \le a_1 < 6</math> and <math>12 \le a_6 < 18</math>, :(2) <math>1..."2020-09-01T15:58:30Z<p>Created page with "==Problem 15== Find the number of integer sequences <math>a_1, a_2, \ldots, a_6</math> such that :(1) <math>0 \le a_1 < 6</math> and <math>12 \le a_6 < 18</math>, :(2) <math>1..."</p>
<p><b>New page</b></p><div>==Problem 15==<br />
Find the number of integer sequences <math>a_1, a_2, \ldots, a_6</math> such that<br />
:(1) <math>0 \le a_1 < 6</math> and <math>12 \le a_6 < 18</math>,<br />
:(2) <math>1 \le a_{k+1}-a_k < 6</math> for all <math>1 \le k < 6</math>, and<br />
:(3) there do not exist <math>1 \le i < j \le 6</math> such that <math>a_j-a_i</math> is divisible by <math>6</math>.<br />
<br />
==Solution==<br />
<math>302</math><br />
<br />
==See also==<br />
{{CIME box|year=2020|n=I|num-b=14|after=Last problem}}<br />
<br />
[[Category:Intermediate Combinatorics Problems]]<br />
{{MAC Notice}}</div>Jbala