SimReal: Matematikk - Game - Info

You have two real dices (cubes).
Throw these two dices and notice the value of each of them.
Select one of the dices and multiply this valye by 2.
Add 5 to the result.
Multiply the result by 5.
Add the value of the other dice to the result.
Write the result in the datafield.

An example:

The values of the dices are 2 and 4.
We select one of them, for example 4.
We multiply the value (4) of this dice by 2, that is 4*2 = 8.
Then we add the number 5, that is 8 + 5 = 13.
We multiply the result (13) by 5, that is 13*5 = 65.
Then we add the value (2) of the other dice, that is 65 + 2 = 67.

This result (67) we write in the grey field in the control window.

Think of a number consisting of two digits.
Let us choose the number shown as an example in the simulation window, that is the number 35.
Add the two digits (3 and 5) of this number, that is 3 + 5 = 8.
Subract the last solution (8) from the first number (35), that is 35 - 8 = 27.
Find the answer (27) i the number form to the left in the simulation window and notice the symbol (figure) to the right of this number (27).
Then click on the blue disc in the simulation window.

You 3 pins and n discs on the left pin, the smaller ones on the top.
You are going to move these n discs to the right pin:
- Move only one disc at a time.
- Only the disc on the top can be moved.
- A disc can not be placed on the top of a smaller one.
- All the 3 pins can be used.

The number n of discs in the interval [0,6] can be set by the scrollbar (default n = 3).
'Move' sbows the number of movements.
'Min' shows the minimum number of movements.
The minimum number of movements for n discs is 2^n-1.

Recursive Figures:

Drawing 4 different fractal figures by recursion:
- Triade
- Quadric
- 2Dim
- Tree

Select a figure by the associated checkbox.
Use the scrollbar to decide the minimum structure of the figures.

We have 3 doors.
A car is placed randomly behind one of the doors.
Behind the two other doors there is an orange.
You want to open the door where you can find the car.

Select a door by the help of the checkboxes below the doors.
After selecting a door, one of the door with an orange is opened.
You can choose if you still want to select the door you selected first or you can change to the other door if you want.

Try to find out what is best:
- Still choose the same door you selected first
- Select the other door

Pushbuttons in the application:
- Help Door: Open a door where you find an orange
- Change Door: Change to the other door
- Open Doors: Open all the doors to see the solution
- New Random: Randomly place a car and oranges behind the doors again

You can choose if you want to do this manually ('Manual') or automatically ('Auto').
If automatically, the you can choose if you want to change the door always.
If automatically, you can select if the process should run continously ('start run') or you can see one step at a time ('step forward').

The director of a prison offers n prisoners on death row, which are numbered from 1 to n, a last chance.
In a room there is a cupboard with n drawers (boxes or doors).
The director puts in each drawer the number of exactly one prisoner in random order and closes the drawers afterwards.
The prisoners enter the room one after another.
Each prisoner may open and look into n/2 drawers in any order and the drawers are closed again afterwards.
If during this search every prisoner finds his number in one of the drawers, all prisoners are pardoned.
If just one prisoner does not find his number, all prisoners have to die.
Before the first prisoner enters the room, the prisoners may discuss their strategy, afterwards no communication of any means is possible.
What is the best strategy for the prisoners?

If there are n = 100 prisoners and every prisoner selects n/2 = 50 drawers at random the probability that a single prisoner finds his number is 50%. Therefore, the probability that all prisoners find their numbers is the product of the single probabilities which is 0.5¹⁰⁰ = 0.0000000000000000000000000000008, a vanishingly small number.
In the simulation application there are 8 prisoners, but also there it's a very small number:
0.5⁸ = 0.0390625.
The situation appears hopeless for the prisoners.

Surprisingly, there is a strategy which gives the prisoners a survival probability of more than 30%.