In this article, we examine the existence of nice arrangements of stars on the Ameri- can flag. We show that despite the existence of such arrangements for any number of stars from 1 to 100, with the exception of 29, 69 and 87, they are rare as the number of stars increases. 1. INTRODUCTION. The Union Jack is the blue, upper left portion of the American flag that contains a star for each state in the Union 1 . From 1777 to 2002, the Union Jack was the maritime flag used by American Navy vessels to establish their nationality. With the passage of the Puerto Rico Democracy Act by Congress in 2010, the door has been opened for Puerto Rico to set a referendum which could result in it becoming the 51st state. By law, each time a state is admitted into the Union, the government must create a new Union Jack with an extra star by the fourth of July following the admittance of the new state. In a recent Slate article (8), Chris Wilson considered this possibility and raised the question: What might a 51 star Union Jack look like? The current 50 star jack design is usually credited to Robert G. Heft (7). In 1958, when the debate over Alaska's statehood status was being considered, Heft claims to have guessed correctly that Congress would eventually allow Alaska to join the Union only if Hawaii was admitted as well. Back then Alaska was Democrat territory, while Hawaii was more Republican, so admitting both would maintain the current balance of power in Congress. While some designers were working on a 49 star arrangement, Heft had already created a 50 star arrangement one year ahead of Hawaii becoming the 50th state (see Figure 1).
['Dimitris Koukoulopoulos', 'Johann Thiel']
Arrangements of Stars on the American Flag