3. A safe is locked by a combination of of four binary digits (that is, 0 or 1), but the owner has forgotten the combination. The safe is designed in such a way that no matter how many digits have been pressed, if the correct combination of three digits is pressed at any point, then the safe automatically opens (there is no "enter" key). Our goal is to find the minimum number of digits that one needs to key in in order to guarantee that the safe opens. In other words, we wish to find the smallest possible length of a binary sequence containing every four-digit sequence in it. (a) Create a digraph whose vertex set consists of three-digit binary sequences. From each vertex labelled ryz, there is one outgoing edge (labelled 0) leading to vertex yz0, and another outgoing edge (labelled 1) leading to vertex yz1. (b) Explain why every edge represents a four digit sequence and why an Eulerian tour of this graph represents the desired sequence of keystrokes. (c) Find the minimum number of digits that one needs to key in to guarantee that the safe opens.

In the Dice Roll game, the player begins with a score of 1000. The player is prompted for the numberof points to risk and a second prompt asks the player to choose either high or low. The player rollstwo dice and the outcome is compared to the player’s choice of high or low. If the dice total is between2 and 6 inclusive, then it is considered “low”. A total between 8 and 12 inclusive is “high”. A total of7 is neither high nor low, and the player loses the points at risk. If the player had called correctly, thepoints at risk are doubled and added to the total points. For a wrong call, the player loses the points atrisk. Create a DiceRollGame application that uses a DRPlayer object based on this specification. TheDRPlayer object should have two Die member variables that represent the dice. The Die class shoulduse a random number generator to determine the outcome in a roll() method. Application outputshould look similar to:

Can u solve this ?

Flashback to Probability:  Determine the odds of rolling TWO 6-sided dice, and getting a total between the two dice that is a multiple of three.

Blue-Eyed Island: A group of individuals live on an island until a visitor arrives with an unusual order: all blue-eyed people must leave the island as quickly as possible. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person does. How long will it take for the blue-eyed individuals to leave?

A flight of stairs has 10 steps numbered 1 to 10 as shown in the figure below. i. How many ways could you climb up the set of stairs, assuming that you can skip any number of stairs with each step, but you must end on step 10 and you can only go up, never down and never remaining on the same step. ii. How many ways could you climb up the set of stairs, assuming you take exactly 4 steps. Again, your staircase climb ends on step 10. JAlthough there are different ways in which you could solve this problem, model the problem as a balls and bins problem for full credit.

Data Generator Most application depends on data. In IoT data is collected/generate by sensors. Since, we do not have access to sensors, we will have to generate data via code. The plotting a sufficient number of these data points (500 in this case) should get the following diagram or something very similar:   You will pick a quantity that you would like to simulate (such as temperature, humidity, barometric pressure, customers arriving at a mall, or just with an alternate descriptor) and decide what shape you will emulate.  This will guide you in selecting sensible value base lines for your data values. e.g., If you pick inside temperature then normal range will be 18-21oC. Design and build a class that will model your sensor reasonably well.  Notice how the peaks do not occur at regular interval, nor are they the same height. Even the squiggles are the same shapes. You will create a class with a single public member (property) that give you a “random” value in your intended range and…

Write in Java please