# Fitness and maths!

Done 3 sets of 800 meters for PT today. Each with a 30second rest period inbetween. I was in the fast group, of three groups, and coming in the first few positions in the fast group for each run. First time, I done it in 2 minutes 30, second time in 2:44 and third time in 3:00. Not including the rests (which of course sped up the average time) I done 2.4 km in 8:14, that's about a mile and a half.

And all that after doing a few miles for boxing training at 6am as well! A few miles and a hundred or so pressups! The staff didn't quite think out the pressup routine... we ran down a street, each time we passed a lamppost we would do some pressupts. 1 at the first lamppost, 2 at the second, 3 at the third, etc. However there were 20 lamp posts. The total pressups would have been 210... but NO-ONE kept it up! We sprinted inbetween each lamp post, after the first 10 lamp posts I'd done 55 pressups and then slacked off as did many others. My upper body isn't as good as my running.

The formula to calculate the total number of pressups we were supposed to do is (n + 1) * (n/2) (The maths: Assuming an even number of lampposts, you pair up opposite lamp posts, so between the first and last lamp posts you'd do 1 + 20 pressups (21), the second and second to last you'd do 2 + 19 = 21, the third and third to last you'd do 3 + 18 = 21... this way, you get 10 pairs of 21 pressups = 210 pressups). As a formula that is number of pressups = number of lamp posts (n) + 1, times by half the number of lampposts. total = (n+1) * (n/2). This formula works for any sequence where you are adding up numbers that go up in ones... 1 + 2 + 3 + 4 + 5 + 6, etc, so at 10 lamp posts I'd done (10 + 1) * (10/2) = 11 * 5 = 55 pressups. (If the total number of elements is ODD, the formula doesn't work because you can't properly pair an odd number of items. Then, you remove the middle number, apply the formula, then add the middle number to the result.
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