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2008 AMC 10B Problem 23

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2008 AMC 10B Problem 23AMC 10 Step by Step

Name: Date: September 13, 2026

Diophantine Equations · difficulty 4 of 5 · about 5 min · position P21-25

A rectangular floor measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$ . An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair $(a, b)$ ?

A)
$1$
B)
$2$
C)
$3$
D)
$4$
E)
$5$

2008 AMC 10B Problem 23

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