Here is the US Army Herald Trumpets playing a rousing fanfare:

……………………………………………………………

Marching Maths

Three nations are marching one after the other:

Pajamaramas (PJ Boy flag bearer),

The Crytomanians (Mummy’s Boy flag bearer)

and the Berserkers (Olag the Viking flag bearer).

But there is a problem.

They march around the Olympic Track, which is a 400m circuit (inside track).

Lego Olympic Track Circuit = 400/50 = 8 m

But the Pajamaramas, the Cryptomanians and the Beseerkers all walk at different speed. They could just bump into one another and end up in a big heap. So how much time should the officials allow between each country so they don’t collide on the track.

…………………………….

Speed S_{1}

PJ Boy is a really slow walker

Real life Really Slow walk = 3.0 kph = 3000 m/hr

……………………………………………….= 3000/60 = 50 m/min

Lego really slow walk= _{ }50/50 = 1 m/min

Speed PJ Boy = S_{1 }= 1m/min

……………….

Speed S_{ 2}

Mummy’s Boy is a slow walker

Real Life Slow walk = 4.5 kph = 4500 m/hr

…………………………………. = 4500/60 = 75 m/min

Lego slow walk = 75/50 = 1.5 m/min

Speed Mummy’s Boy = S_{ 2}_{ }= 1.5 m/min

……………………………..

Speed S_{3 }

Olag is a fast walker

Real life fast walk = 6 kph = 6000 m/hr

……………………………… = 6000/60 = 100 m/min

Lego really slow walk = 100/50 = 2 m/min

Speed Olag = S_{3 }= 2m/min

Lego Track Circuit = 8m

Time on circuit (T) in mins:

T = d/S

T = 8.0 /S

The time each nation takes to finish marching around the track will be:

If you started them all at once there’d be a real pile up.

March Time with 1 min gap between groups:

The Enforcer from the Constellation Obeymia will make sure each marching group leaves exactly on time. He will set the clock ticking at 0 mins then enforce a one minute gap between each group.

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Look at the times each nation finishes marching around the track now:

PJ Boy…………………………………………………………………………..

and the Pajamaramas ……………………………………………..8 mins,

Mummy’s Boy and the Crytomanians ………………. 6 mins 20 secs

and Olag and The Beserkers start 2 minutes after PJ Boy and Co and finish at …………………………………. 6 mins.

They will still collide on the track!!!!!

Here are the results for different gap times:

Nation

March Time

Gap time

0 min

March Time

Gap Time

1 min

March Time

Gap Time

2 min

March Time

Gap Time

3 min

PJ Boy + the Pajamaramas

8

8

8

8

Mummy’s Boy and the Crytomanians

5mins 20 secs

6 mins 20 secs

7mins 20 secs

8 mins 20 secs

Olag and The Beserkers

4

6

8

10

The 3 minute gap works!!!

I think we need a round of applause:

Why not ALGEBRA?

If you had to do this calculation for the entire 205 nations at the 2012 Olympic Games, you can see that your brain might explode.

Da-DA! We can use algebra.

Here is a formulae:

T = d/S + nt_{g}

where

T = time (mins)

from beginning of ceremony.

d= track circuit distance = 8 m

S = speed m/min

n = nation march order number = 0,1,2,3,etc

t_{g }= time gap between nations (mins) = 1, 2, 3, 4 etc

The closing ceremony is chaos. All the athletes crowd together.

There is one last lot of calculations, mathspigs.

Think about this.

% Gold Medal Winners:

At the 2012 London Olympics there were 47 Gold medals awarded in athletics.

There will be 2,000 athletes competing for these medals. Now some athletes will win more than one Gold medal and some events eg. the relay race involve more than one athlete. Each member of the winning relay team wins a Gold Medal.

Approximately what % of athletes won’t win a Gold Medal at the London Olympics?

Ans: 97.65%

Probability of Winning a Gold Medal:

Ha-HA! Tricked ya! Such a calculation would be meaningless.

The core to all probability is, or should be, RANDOM SELECTION.

Lottery balls fall randomly into the tube. But the Olympic athletes represent a BIASED SAMPLE. Athletes are selected for the games. They must qualify for an event. They train. The chance of one athlete winning is quite different from that of another.

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Eight numbered 100m-sprint athletes is a Biased Sample.

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Eight numbered lottery balls in last nights draw make up a random sample.