#thisweeksfiddler Miles Probability 3 17/256 3.5 32/256 4 24.75/256 4.5 72/256 5 9.1875/256 5.5 33/256 6 20.0625/256 6.5 48/256 Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256 = 19933/4096 ~ 4.8665 miles

#ThisWeeksFiddler EC: W= $90 cash with 50% likelihood from the outset. First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers. After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.

#ThisWeeksFiddler colab.research.google.com/drive/1zobjk...

#ThisWeeksFiddler Arrange circles on a triangular lattice, each surrounded by six other circles. Centers are integer linear combinations of: v1 =(1,0), v2 = (1/2, sqrt(3)/2). Avg area contributed by each surrounded circle = sqrt(3)/2 For large N, min area of region is ~ sqrt(3)/2 N