Happy 𝜋 Day!

Happy 𝜋 Day!

Happy 𝛑 Day! What better day to celebrate our favorite, familiar, fantastic irrational number? This 𝛑 Day we are bringing you a 𝛑-centric approximation activity, a detailed explanation of why this activity approximates 𝛑, and a special bonus math problem and solution (in case you want to spend your 𝛑 Day doing math, math, and more math :) ).

... And Now for Some Math

... And Now for Some Math

At BEAM Discovery the 100 Problem Challenge encourages students to work collaboratively; this past summer students earned a badge for completing a problem from this list of intriguing, puzzle-like problems. We can’t offer you a badge, but this one is pretty satisfying to solve, so give it a whirl!

Fill in each of the hexagons below with a positive integer so that the number in each hexagon is equal to the smallest positive integer that does not appear in any of the hexagons that touch it.

...And Now for Some Math

...And Now for Some Math

Here’s a math game you can play while keeping up social distancing. Find someone to play with and read on.

The game:

You are given $20, and you must guess a whole number between 1 and 700. For each incorrect guess you make, you must pay $1, and then you are told if you were over or under the correct number. If you guess the number, you get to keep the money you have left.

Challenge 1: Can you guarantee a profit on this game? What's the greatest profit you can guarantee even if you are very unlucky on your guesses?