The n-camel stack problem
Lucy Rycroft-Smith &
Darren Macey
Who are you?
Probability vs Intuition
At the start, what is the probability of a 5 camel
In the first ‘turn’ what is the
stack occurring?
1
1
1 probability
1
of a 5-camel
a)
b)
c)
d)
81
243
3 stack occurring?
27
At the start, what is the probability of no stacks
occurring?
1
1
1
a)
b)
c)
0
d)
If n camels start in a full n81
2
3
3𝑛
243
stack,
what
is the
At the
start,
what is the probability of an n-stack
probability
theynend
occurring,that
where
is the number of camels?
the turn
1𝑛−1on an1 n-stack?
1𝑛
13
a)
b)
c)
d)
3
𝑛
The big question…
If n camels start in a stack on the same square,
what is the probability that after x legs, they finish
in an n-stack?
•
•
•
•
How would you get started?
What simpler questions might you ask first?
What variables might you fix?
How can the maths be represented?
Representations
Simulation elation!
2 camels, 2 turns, no stacking, no problem!
Stack
no stack
0
0
Launch
Simulation
2 camels, 3 turns, no stacking, no problem!
Stack
no stack
0
0
Launch
Simulation
Not so trivial now…
2 Camels, with stacking
Number of trials
number of rolls
1
2
Start
810
2
1
Launch
Simulation!
No stack
Stack
598
212
2
1
2
3
2
1
4
2
5
6
7
8
9
10
11
12
Not so trivial now…
3 Camels, with stacking
Number of trials
number of rolls
810
2
1
2
3
Start
2
1
1
2
1
2
No stack
Stack
766
45
Dice rolls
1
3
3
2
5
4
3
6
7
Run Simulation
1
3
1
3
3
8
9
10
11
12
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