Trick 10: Math Mentalist Devises Foolproof Gambling System

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Math Mentalist Devises Foolproof Gambling System

Requirements: Smart board/Data Projector

or Chalk & Talk

This is the most awesome way to introduce probability.

Mentalist Derren Brown devises a foolproof gambling system. He sends a girl , Kadisha, the number of a winning horse in race to be run the next day. It wins. He sends her the winning horse and race number 4 more times. She ends up with winnings close to £ 1000 before the final race. Derren convinces her to borrow money for the last bet. She does. She places £4,000 on a horse. Did it win?????

Watch Part 5 of The System

 

 

If you are not convinced Derren Brown can come up with a foolproof system for horse race tipping, let me explain The System. He took 7,776 e-mail addresses, divided them into 6 equal groups and sent each group a different number for a horse in a 6 horse race to be run the next day. Naturally, one group of 1296 had been given the winning horse number.  This group was divided into 6 again and given the number of the ‘winning’ in a six horse race the next day and so on.

Race 1: 7776

Race 2: 1296

Race 3: 216

Race 4: 36

Race 5: 6

Out of 7776 punters, only one punter was given in advance five horse race winners in a row. Was it Kadisha. You will have to watch the Youtube above.

You can watch THE SYSTEM in full here. It takes 47 mins.

Get Ready for the Lego Olympics

Get ready mathspigs. You need one Lego Man, Girl, Vampire or Alien each for this exercise. Now we are going to set out the Lego Olympics Athletics track.

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But this story of the Olympics begins with Carl Lewis, one of the greatest athletes of all time who won 9 Olympic Gold medals in 100m, 200m, relay and long jump.

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Carl Lewis

Mathspig needs to find out how big the Lego Olympics track would be. How? Easy.

Carl Lewis will be our standard Lego Man.

I chose Carl Lewis because he kindly gave me his autograph once when I sprinted in high heels across a ballroom floor at a sports dinner in Melbourne and beat all other journalists.  It was my personal best in high heels, I think.

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This means everything at the Lego Olympics  will be

1:50

of the real Olympics.

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The  Lego Bird’s Nest Stadium @ Beijing will be 1/50th of the real Bird’s Nest Stadium. (Not the scale shown here). Pictures by Johor Bahru.

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The Lego Beijing Water Cube Swim Centre will be 1/50th of the Real Water Cube.

EXERCISE 1:

Now mathspiggies over to you. The first thing to do is calculate the Lego Olympic measurements (table below). 

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EXERCISE 2:

Then mark out a Lego Olympics 100m sprint to scale and/or

draw a Lego Olympic track (in chalk, perhaps) and/or

step out a Lego Olympic marathon track and/or

make a pole vault pole to scale for your little Lego Man.

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Structure	Real Olympics	Lego Olympics
100m Sprint	100m	2m
400m Sprint	400m
42 km marathon	42,000m
Olympic Pool Length	50m
Olympic Pool Width	25m
Olympic Rowing Course	2,000m
Equestrian Jump Height	2m
Approx Pole Vault Pole Length	5.5m
Javelin Length Men Women	2.6m 2.2m
Olympic Stadium Straight Segment Semi-circle Radius inner Lane Lane Width	84.39m 36.50m 2.5m

Lego Olympics Flags

The Lego Marching band is rehearsing for the Opening ceremony.

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Here are just a few of the weird and wonderful folk from the many planets and nations represented at the Lego Olympics:

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………….Bandito (Republic of Baddies)

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Mr Boopy (Bozonia)

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Gorilla Suit Guy (Halloweenotopia)

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………………..Barry the Butcher (Alien Steakistan)

……………..BioHaz (Toxorama)

…………………Dead-Eye Doc (AyeAwArghia)

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Dr Jabb (Bummerville)

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Hula Lula (Grinmania) 

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1. Flag Fractions

EQUIPMENT: Mixed Lego Blocks

Here is the maths. It’s fractions. It’s simple.

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A. National Flag of  Comotosia

They’re a bit sleepy in Comotosia so you better design a flag to wake them up, mathspigs.

The flag must measure ………….   6 blocks x  12 blocks.

One block is a 4 bumps blocks (See pic). An 8 bumps block equals 2 blocks.

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Here’s the catch, mathpiggies.  1/4 of the blocks in the flag must be RED.

How will you do this? (Hint below)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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.B. National Flag of Bordom

Once again the Bordonians need a lively flag.

The flag must measure 6 blocks by 12 blocks, but this time it must contain 1/4 red and 1/3 blue. How do you do this?

Hint: Mathspigs! You will have to count the number of red and blue blocks.

 

2. Design A National Flag to Lego Scale

First, name your Lego man, girl or alien and pick a name for their country, planet or crypt.

You will be drawing two flags.

All national flags are rectangles except Switzerland and Tibet, which have square flags but not at the Olympic Games.

Olympic Flags measure:  150 cm x 90 cm

or …………………………….. 60 inches x 35 inches.

These sizes are not equal so which flag is bigger the decimal flag or the Imperial Units flag?

The Imperial units flag is 152.9 cm x 88.9 cm. It turns out the area of the Decimal flag is 13,500 cm² and the Imperial Flag 13,593 cm² . 

You will be designing a decimal flag.

Note the Flag ratio of length: width = 150 : 90

…………………………………………………… =  15 : 9 = 5: 3

First design a flag with 5: 3 ratio.  One measuring 10cm x 6 cm would be ideal.

 

BUT

How big are the national flags at the Lego Olympics:

Real flags at the Olympics =  150 x 90 cm

Lego Flag measurements =  150/50 x 90/50 = 3 cm x 1.8 cm = 30mm x 18 mm

Here are my two Lego people with flags  I prepared earlier:

The Enforcer from the Constellation of Obeymia and Mr Boopy from Bozonia.

Lego Olympic Opening Ceremony

The Lego Olympics must begin with a

triumphant Trumpet Fanfare.

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

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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.

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Speed S₁

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 = S₁ = 1m/min

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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

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Speed S₃ 

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 = S₃  = 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:

T₁ = 8.0/S₁  = 8.0/1  = 8 mins

T₂ = 8.0/S₂ = 8.0/1.5 = 5.3333 = 5 mins 20 secs

T₃ = 8.0/S₃ = 8.0/2.0 = 4 mins

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    

TRY IT, mathspigs!!!!!

Lego Olympics Triathlon

This is the Lego Triathlon.

And, mathspiggies, your Lego Man/girl/alien has made it into the finals. 

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EQUIPMENT: Your Lego Man, girl, alien, your brain, a calculator & one dice.

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In the Olympic Triathlon contestants:

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Swim 1.5 km = 1,500 m

Cycle 40 km = 40,000 m

Run 10 km = 10, 000 m

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In a Lego Olympic Triathlon little Lego men, girls, aliens have to:

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Swim 1,500/50 = 30m

Cycle 40,000/50 = 800m

Run  10,000/50 = 200m

But each contestant will be better at some section than another.

Your Lego man, girl, alien replaces one of the following contestants. Transfer their number and times to your column.

Now calculate the Total Times for each contestant.

THEN roll the dice.

3. Disqualified because your coach gave you an alien Smoosnot drink with banned drugs by mistake.

5. Disqualified because a Groppanator from the Urgastor Galaxy ran out of the crowd just before the finish line and hugged you with his 6 arms.

Triathlete	30 m Swim Speed + Time	800m Cycle Speed + Time	200m run Speed + Time	Total Time mins	Roll 3 or 5 Disqualified
1 Mummy’s Boy from Crytomania	40 m/hr ……………	400 m/hr ……………	250m/hr ……………	………….	…………..
2 PJ Boy from Pajamarama	30 m/hr ……………	200 m/hr ……………	500 m/hr ……………	………….	…………..
3 Olag from Beserk	40 m/hr ……………	200 m/hr ……………	500 m/hr ……………	………….	…………..
4 Dead-Eye Doc from AyeAwArghia	60 m/hr ……………	400 m/hr ……………	450 m/hr ……………	…………..	…………..
5 Hula Lula from Grinmania	50 m/hr ……………	400 m/hr ……………	500 m/hr ……………	………….	…………..
6 Mr Boopy from Bozonia	30 m/hr ……………	600 m/hr ……………	200 m/hr ……………	…………..	…………..
7 Gorilla Suit Guy from Halloweenotopia	50 m/hr ……………	500 m/hr ……………	300 m/hr ……………	…………..	…………….
8 BioHaz from Toxorama	60 m/hr ……………	500 m/hr ……………	400 m/hr ……………	…………..	…………..
………………… from ………………..	…………… + ………………..	…………….. + ……………..	…………….. + ……………..	…………..	…………..

Who won?

You can work it out mathspigs.

Total Times are published @ the end of The Lego Olympics Closing Ceremony.

Lego Olympics Closing Ceremony

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 will be 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.

This brings us to the end of the Lego Olympics.

We will finish with this end song by Lego Rock Band and some Lego fireworks.

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Lego Olympics Triathlon total Times: 1. Mummy’s Boy: 3 hrs 33 mins, 2. PJ Boy 5 hrs 24 mins, 3. Olag 2 hrs 51 mins, 4. Dead-Eye Doc 2hrs 57 mins, 5. Hula Lula 3 hrs, 6. Mr Boopy 3 hrs 20 min, 7. Gorilla Suit Guy 2hrs 52 mins,8. BioHaz  2 hrs 36 mins.

Can a Formula 1 car drive upside down? Can an ordinary car fly?

The 2010 Grand Prix is about to hit Melbourne next month so this week, mathspigs we are going to look at car aerodynamics. There are two factors in car aerodynamics. Lift(L) and Downforce(D)

LIFT (L)

Car designers didn’t worry about aerodynamics until the sixties when cars could go fast enough to experience aerodynamic lift, which naturally, reduced tyre traction.  Skirts are added to cars to not only reduce this lift but also create a ‘suction’ (Bernoulli Effect”) under the car.

Here is the Chevy ’69 Camaro from Camaro Untold Secrets.  At 115 mph ( 185 kph which is not only fast but over street speed limits!!!!!) it experienced a front Lift (L) of 375 lbs or pound force.

We’ll simplify the aerodynamics and assume this graph is a parabola as follows.

NB: the only units to use in this equation are L (lb force) and v mph.

Once you know this equation you can calculate the velocity required for a ’69 Camaro to leave the ground due to front Lift (Assume once the nose lifts the downforce no longer applies ie. equals zero.)

We know the weight of the ’69 Camaro = 3,675 lb.

So mathspigs if the ’69 Camaro can go fast enough so that the front Lift equals its weight, it will fly!  At what speed will ’69 Camaro fly?

Downforce (D)

The ultimate design in car aerodynamics is the F1 racing car.  The Downforce (D) on the car is created by the front and rear wings, which work in reverse to aeroplane wings pushing down on the car) and the underbody gap which crates ‘suction’ by the Bernoulli effect.

 

Williams FW31 weight including driver  605 kg

      

                

                                                                                                                                                                                                   Renaut R30 total weight 605 kg

                                

      

Toyota TF 109    weight 605 kg                                                                                                                                                                                                                                                       

                                                                                                                                                                                                                                          BMW Sauder C29    620 Kg

 

 

Ferrari F60    605 kg

Downforce is approx:

35% rear wing

25% front wing

40% defuser on underbody

While downforce equations are complex ( See Wikipedia ) they approximate to the following equation for a standard F1 car design:

Could the Downfoce (D) on a F1 car exceed its weight so that it could drive upside along a … very long tunnel? I’m thankful to New Scientist (Aerial Glue 20 Jan 2010) for this insight.

Now mathspigs you have the mass of F1 car above so you can calculate the speed at which a typical F1 racing car could drive on the roof of a tunnel glued to the ceiling by its own downforce.

NOTE: This equation only works for a limited range of car mass, m. You can’t reduce m by dumping bits of the car. Likewise, if you add bits to the car to increase m eventually the aerodynamic constant, k, will change.

Does the weight of a driver make a difference?

Mathspig did stand in the pits in the Australian Grand Prix in Adelaide in the ninties ( with a borrowed ticket) not far from Ayrton Senna (Right. Tragically killed in 1994) and I was shocked to see how small he was. His height is recored at 171 cm but that is Mathspig’s height and he was shorter.  Today while some F1 drivers are over 6 ft (183 cm) including Australia’s Mark Webber (Right) most are not tall and, therefore, not that heavy.

When the KERS (Kinetic Energy Recovery System), which stores braking energy, was introduced 2009 drivers lost weight to accommodate system.

Nico Rosberg 76 kg to 66 kg

Kubica 78 kg to 70 kg

Heidfeld  56 kg to 59 kg

While Trolli, Hamilton and Vettel reduced their weights to 64, 67 and 62.5 kg respectively.  More info

Typically, a driver will lose 5 kg just competing in a Grand Prix.  IF the driver dropped 15 kg would that effect the upside down speed of an F1 racing car?  Drop the mass (m) value above and see if it makes much of a difference.

Or, instead, if your School Principal was driving the F1 racing car ( Assume an average  F1 driver weighs 65kg. How much heavier is your Principal to an F1 driver? Guess.) Increase the mass (m) in the above equation by this amount and you can calculate the speed  at which your school principal and F1 car would drop off the tunnel ceiling.

Meanwhile, even Mythbusters hasn’t tested this stick to the ceiling theory. Why?

Even the slightest bump on the ceiling could disrupt the underbody ‘suction’ and down goes the $zillion car and driver upside down and at speed.

This hasn’t stopped some Youtube mockups of F1 cars driving on the ceiling!!!

More Maths. No Sweat!!!

 Mathspigs there are two things that stop kids doing maths. Fear & boredom. But we are going to show NO FEAR. You may find some of these equations a bit scary. I do too. But I can make some sense of some of this stuff. Here goes.

 The article No Sweat. Well, not as Much as You think (New Scientist 18/7/09 #mce_temp_url#  ) highlighted research by the US army into finding an equation for how much men and women sweat. They need this information so they can calculate how much water they need to carry. Makes sense.

 The full research paper by Sawka & Co can be downloaded for free from The Journal of Applied Physiology #mce_temp_url#  . 

 How do they calculate how much you sweat???

Basically, they use NUDE body mass work out how much weight you lose after exercise. Allowances are made for mass (or weight) by breathing in oxygen and breathing out water & carbon dioxide. 

They can also calculate how much heat is lost when you are nude if  m  ( or m with a little dot) is your sweat rate in grams per hour.

 

 

 

 

 

 Then things go a little crazy. Here’s one part of the equations for heat lost when dressed. I just want you too see how crazy some equations can be.  We’re not going to use it. But when you are doing studies like this you get used to such equations.

 

 

 

 

 

 

 

ARE WE SCARED, MATHSPIGS? No. We’re going IN to look at the results. We can make sense of them.

 

Thanks to Dean Van DEn Heuvel, Kyneton, Victoria for this fab math pig pic. We like happy mathspigs!!!!

 

When you read the table below keep in mind:

 

 

How much do you sweat????

Here’s your answer!!!!!!!

 

 

With one more piece of data you can calculate how much you would sweat in Battle Dress Uniform or body Armor plus vest. Your surface area:

“Normal” BSA is generally taken to be 1.73 m² for an adult. ( More @ Wikipedia: #mce_temp_url#)

Average BSA values
Child 9 years	1.07	m²
Child 10 years	1.14	m²
Child 12-13 years	1.33	m²
For men	1.9	m²
For women	1.6	m²

Which sport is more DANGEROUS to play? Cricket or baseball?

Mathspigs you are about to be hit on the head with some BALL PARK figures. There is so much maths involved in comparing cricket and baseball I hardly know where to begin. So I will just set you up with comparitive statistics for starters. Here they are:

 

 

 

 

You now have sufficient information to calculate the following:

Q1. If a cricket player  makes 4 runs (and runs between the wickets) and a baseball player hits a home run, who runs the furtherest?

Q2. What are the delivery ball speeds of an average pitcher and a mid paced bowler in m/sec?

Q3. How far would the delivery of an average pitcher and a  medium paced bowler travel in 10 seconds?

 Q4. If Shoaib Akhar fielded a ball in cricket 20 m from the wicket when the batsman was still 8m from the wicket (A typical running speed for humans is 32 km/h) would he be able to run him out?

 Q5. How long would it take a ball thrown by Joel Zumaya to reach the batsman if the pitchers mound was exactly in the middle of the baseball square?

 Q6. Which sport is more dangerous? We will base our calculations on the speed (or velocity) and the weight (or mass) of the ball. We must use the same units in all calculations. For each sport plot x-axis: velocity of ball (v) against y-axis mass x velocity (mv) of the ball. mv is the momentum. In ballistics the change in momentum is called the IMPULSE (impact for us). If you are hit on the head with a ball it is the change in momentum of the ball that does the damage. A small ball at a high speed can do as much damage as a larger ball at a slower speed. We are not including spin, curve balls or air resistance to keep calculations straight forward … literally!!! 

Now that you have your graph you can answer these questions:

Q6a. Which sport for professional players is the most dangerous? 

Q6b. At what speed does a cricket ball do the same damage as a baseball? Show three examples. (Hint: Draw a straight line from the Y-axis)

 

 

Pics: Tim Lincecum (Left) with 101 mph pitch, Shane Warne (Upper Right) and Shoaib Akhtar (Lower Left)

How much do the most expensive football players in the world cost per kg?

Ricardo Izecson dos Santos Leite (born April 22, 1982 in Brasília, Brazil), simply known as Kaká, is a Brazilian footballer who plays as a midfielder.

Last week it was announced that Real Madrid  had paid Kaka’s current club, AC Milan €65 million ($114.5m) for the soccer player.

This is the second highest payment in football history as  the record transfer deal was set by Zinedine Zidane when he joined Madrid from Juventus for €75m ( $ 132.1 m) in 2001. (Sydney Morning Herald 10 June 2009 #mce_temp_url# )

 

 

 

 

               Kaka Weight =  73 kg

               Zidane weight = 78 kg.

          Now mathspigs you have enough information to calculate how much these soccer players are worth per kilo. 

           You can use a table, a picture graph or a bar graph to compare the costs of these footballers per kilo with other products available on the market today. Don’t forget mathspigs football players are bought and sold like commodities so this is a reasonable comparison to make:

platinum = $46,700 per kilo

  gold = $37,500 per kilo

 silver = $ 560 per kilo

Tic Tacs = $ 44.44 per kilo (Confectionery costs from grocery.bestpricedirectory #mce_temp_url#

Freddo Frogs = $19.95 per kilo

Meanwhile you can easily work out if Kaka is worth his weight in gold. Or, to put it another way, how many kilo of gold would Real Madrid need if they were to pay for Kaka in gold bullion? Australia actually produces 1 kg gold ingots or bars. So how many gold bars would Kaka cost?

As one of our sayings in English is ‘It cost me an arm and a leg’ you can also work out how much a ‘very upmarket’ arm and leg might cost.

 To do this maths pigs you need to know the approximate weight of a human arm and leg.

According to Wikianswers a human arm weighs approx 3.3 kg.

While according to that great source of information Wii Fit your legs make up 40% of your body weight. So one leg is 20 % of a person’s body weight. You now have enough information to calculate how much an arm & a leg is worth in World Soccer.

Go to it mathspigs.