Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 3"
m (Created page with "== Problem == == Solution == == See also == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}} Category:Introductory Number Thoery Problems") |
m (→See also) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | |||
| + | A <math>\emph hailstone</math> number <math>n = d_1d_2 \cdots d_k</math>, where <math>d_i</math> denotes the <math>i</math>th digit in the base-<math>10</math> representation of <math>n</math> for <math>i = 1,2, \ldots,k</math>, is a positive integer with distinct nonzero digits such that <math>d_m < d_{m-1}</math> if <math>m</math> is even and <math>d_m > d_{m-1}</math> if <math>m</math> is odd for <math>m = 1,2,\ldots,k</math> (and <math>d_0 = 0</math>). Let <math>a</math> be the number of four-digit hailstone numbers and <math>b</math> be the number of three-digit hailstone numbers. Find <math>a+b</math>. | ||
| + | |||
| + | == Solution == | ||
== Solution == | == Solution == | ||
| − | == See | + | == See Also == |
{{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}} | {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}} | ||
| − | [[Category:Introductory Number | + | [[Category:Introductory Number Theory Problems]] |
Latest revision as of 07:14, 19 July 2016
Contents
Problem
A 
number 
, where 
denotes the 
th digit in the base-
representation of 
for 
, is a positive integer with distinct nonzero digits such that 
if 
is even and 
if is odd for 
(and 
). Let 
be the number of four-digit hailstone numbers and 
be the number of three-digit hailstone numbers. Find 
.
Solution
Solution
See Also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
