2015 AIME II Problems/Problem 10: Difference between revisions
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==Problem | ==Problem== | ||
Call a permutation <math>a_1, a_2, \ldots, a_n</math> of the integers <math>1, 2, \ldots, n</math> ''quasi-increasing'' if <math>a_k \leq a_{k+1} + 2</math> for each <math>1 \leq k \leq n-1</math>. For example, 53421 and 14253 are quasi-increasing permutations of the integers <math>1, 2, 3, 4, 5</math>, but 45123 is not. Find the number of quasi-increasing permutations of the integers <math>1, 2, \ldots, 7</math>. | Call a permutation <math>a_1, a_2, \ldots, a_n</math> of the integers <math>1, 2, \ldots, n</math> ''quasi-increasing'' if <math>a_k \leq a_{k+1} + 2</math> for each <math>1 \leq k \leq n-1</math>. For example, 53421 and 14253 are quasi-increasing permutations of the integers <math>1, 2, 3, 4, 5</math>, but 45123 is not. Find the number of quasi-increasing permutations of the integers <math>1, 2, \ldots, 7</math>. | ||
==Solution== | |||
Revision as of 18:24, 26 March 2015
Problem
Call a permutation 
of the integers 
quasi-increasing if 
for each 
. For example, 53421 and 14253 are quasi-increasing permutations of the integers 
, but 45123 is not. Find the number of quasi-increasing permutations of the integers 
.
