Difference between revisions of "2019 CIME I Problems/Problem 9"
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Let <math>\text{N}</math> denote the number of strictly increasing sequences of positive integers <math>a_1,a_2,\cdots, a_{19}</math> satisfying the following two rules<math>:</math> | Let <math>\text{N}</math> denote the number of strictly increasing sequences of positive integers <math>a_1,a_2,\cdots, a_{19}</math> satisfying the following two rules<math>:</math> | ||
* <math>a_1=1</math> and <math>a_{19}=361,</math> | * <math>a_1=1</math> and <math>a_{19}=361,</math> | ||
| − | * for any <math>i \neq j,</math> if <math>b_{ij}</math> is the <math>(i \cdot j)^{\text{th}}</math> number not in the sequence<math>,</math> then <math>( | + | * for any <math>i \neq j,</math> if <math>b_{ij}</math> is the <math>(i \cdot j)^{\text{th}}</math> number not in the sequence<math>,</math> then <math>(a_i-b_{ij})(a_j-b_{ij})<0.</math> |
Find the largest positive integer <math>k</math> such that <math>2^k</math> divides <math>\text{N}.</math> | Find the largest positive integer <math>k</math> such that <math>2^k</math> divides <math>\text{N}.</math> | ||
| + | |||
| + | =Solution 1= | ||
| + | {{solution}} | ||
==See also== | ==See also== | ||
Latest revision as of 15:28, 6 October 2020
Let 
denote the number of strictly increasing sequences of positive integers 
satisfying the following two rules
and 
- for any
if 
is the 
number not in the sequence
then 
and 
if 
is the 
number not in the sequence
then 
Find the largest positive integer 
such that 
divides 
Solution 1
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See also
| 2019 CIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All CIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
