It’s Flag Day here in America, so it’s a great time to talk about all the crazy math our nation’s flag has done. For one thing, it has 50 stars for our 50 states, because each time our country added a new state, we added a star. In the beginning we also tried adding a stripe for each new state. But after adding Vermont and Kentucky (#14 and #15), we realized the flag would turn into a pink blur of teeny stripes. So we went back to 13 stripes and used stars for states after that. Since sometimes a bunch of states joined at once, the number of stars made some big jumps, like from 38 to 43 when we added the Dakotas, Idaho, Montana, and Washington. The current 50-star flag has lasted the longest, but there have been 27 versions in total — and that’s a lot of math to wave around.
Wee ones: If the flag has 7 red stripes and 6 white stripes, which color has more stripes?
Little kids: Since the stripes on our flag are red, then white, then red, then white…what color is the 8th stripe? (Don’t peek!) Bonus: When the flag jumped from 48 stars to 50, how many states had we added?
Big kids: One flag in 1818 had the stars laid out in a star shape: 1 star in the middle, 10 more around it to make a pentagon, and then 3 in each of the 5 points. How many states did we have at that time? Bonus: How many more states would we need today to double that number of stars?
The sky’s the limit: After we had our first 13 stars, for what number of states could we have had by now where the stars could make a perfect square (same number of rows across and down), and where the digits add up to 9?
Wee ones: More red stripes.
Little kids: White. Bonus: 2 more states – Alaska and Hawaii, in 1959.
Big kids: 26 states, since it’s 1+10+15 stars. Bonus: Double would be 52, so we’d need 2 more states.
The sky’s the limit: 36. The only perfect square numbers between 13 and 50 are 16, 25, 36, and 49. 36 is the only one where the digits add to 9 — because it’s the only one divisible by 9!