Maths Mystery Box 5: FANTASY

 

Middle school maths challenge

%, probability and a fight to the death

This problem is trickier than you think. You will need this information.

Major Major HINT

Hunger Games Maths Survivor ANSWER 1

Hunger Games Maths Survivor ANSWER 2

You will find more HUNGER GAMES maths including How long would it take you to bleed to death? here.

The Hunger Games Maths

The Hunger Games is about MATHS. Here are some interesting Hunger Game statistics.

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THE PLOT:

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In Suzanne Collin’s book, The Hunger Games, 12 districts in the land of Panem are suppressed and controlled by a vicious elite, who dress like neon-coloured French courtesans.

Each year the cruel rulers select one teen of each sex between the ages of 12 and 18 from each district to become tributes, who must fight to the death in a televised, sponsor-supported media event called The Hunger Games, set in a staged wilderness.

Only one tribute can survive. Katniss Everdeen and Peeta Mellark from the poor coal-mining District 12 are the local tributes for that year and must play at being star-crossed lovers to gain sponsor support and survive.

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THE MATHS:

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……………………………………………….……..The Reaping…..

Tributes are selected in a process called The Reaping. The names of the, approximately, 2,000 young people in each district are placed in separate barrels for males and females and the names are drawn out of these barrels BUT…

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12 year olds …….. 1 slip

13 year olds ……..  2 slips

14 year olds ……..  3 slips

15 year olds ……..  4 slips

16 year olds …….. 5 slips

17 year olds ……..  6 slips

18 year olds …….. 7 slips

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BUT you can gain extra ‘food’ if you accept for more name slips.

Gale Hawthorne (pictured above), Katnis’ friend from District 12, has 42 slips in the barrel. What are his chances?

We will assume that there are 1,000 male teens and 1,000 female teens in each district and an equal distribution – rounded off – for each age group to 1000/7 = 143 male teens and female teens in each age group.

 

 

Age Group Male or Female	No. Name slips	Total No. Name Slips	Probability of being REAPED	Probability P
12	1	143	1 : 4004	1: 4004
13	2	286	2 : 4004	1 : 2002
14	3	429	3 : 4004	1 : 1335
15	4	527	4 : 4004	1: 1001
16	5	715	5 : 4004	1 : 801
17	6	858	6 : 4004	1 : 667
18	7	1001	7 : 4004	1 : 572
total		4004

 

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Hunger Game: Survival Maths 1

How long can you live if you are bleeding?

Unlike Kill Bill where Tarantino used, literally, hundreds of litres of fake blood (See Mathspig Post: Don’t Bleed Your Fake Blood on Me), The Hunger Games shows very little blood.

Nevertheless 11 tributes are killed violently in the first few minutes of the game and Peeta is wounded later in the movie(pic with Katniss above).

To calculate how long you would last in The Hunger Games if bleeding we must know your volume of blood and the rate of bleeding.

1. How much blood do you have?

According to the BJA, the British Journal of Anaesthesia, blood volume is  7% of body weight in adults and 8 – 9 % of body weight in children.  Doctors are not confusing weight and volume. Blood is very close to the density of water and so 1 litre of blood weighs 1 kg. 

(NB: Future Engineers: Blood does not flow like water as the blood platelets affect the viscosity.)

Using blood volume (in litres) as 8% of body weight (in kg) then typical blood volumes for teenagers would be:

Age Group	Blood Volume litres Female	Blood Volume litres Male
12	4.3	4.0
14	4.7	5.1
16	5.0	6.1
18	5.3	6.6

 

2. How long would you last if bleeding?

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Obviously, it will depend on the rate of bleeding.

According to the BJA massive blood loss equals a blood loss rate of 150ml/min or 50% of blood volume loss within 3 hrs.

 BLOOD LOSS EQUATION:

B = total blood loss ml

R = rate blood loss in ml/ min = 150 ml / min

t = time min

B = Rt

B = 150 t

According to New Scientist loss of blood IN THE AVERAGE ADULT produces the following symptoms:

A  750 ml: feel blood loss

B  1500: weak, thirsty & anxious

C  2000 ml : dizzy, unconscious

D  3000 ml: Dead

See A, B, C and D on graph below.

3. How long have you got?

First, calculate  50% of your blood volume for your age.

Now go to the blood loss graph and see how long it would take you to lose this volume.

You can stop doing the maths now, mathspiggies, and get some help to stop the bleeding.

Hunger Games : Survival Maths 2

Katniss’ weapon of choice is the bow and arrow.

Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.

What angle should she choose?

Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot

 According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.

Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved. 

So we will assume the arrow velocity (V_a) equals horizontal vector speed (V_x). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.

First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.

 NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.

Gravity Eqn in the graph above comes from School for Champions