9
Part of 2022 AMC 10
Problems(2)
Painting a Rectangle
Source: 2022 AMC 10A #9 / 2022 AMC 12A #7
11/11/2022
A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?
[asy]
size(5.5cm);
draw((0,0)--(0,2)--(2,2)--(2,0)--cycle);
draw((2,0)--(8,0)--(8,2)--(2,2)--cycle);
draw((8,0)--(12,0)--(12,2)--(8,2)--cycle);
draw((0,2)--(6,2)--(6,4)--(0,4)--cycle);
draw((6,2)--(12,2)--(12,4)--(6,4)--cycle);
[/asy]
AMCAMC 10AMC 122022 AMC2022 AMC 10a2022 AMC 12Acounting
nice telescoping series
Source: 2022 AMC 10B #9
11/17/2022
The sum
can be expressed as , where and are positive integers. What is ?
AMCAMC 102022 AMC2022 AMC 10B