main part of the train and the white die is a funnel on the engine at the front
ID: 3051560 • Letter: M
Question
main part of the train and the white die is a funnel on the engine at the front of the train. There are three rules for making such a train: 2. The dice model I below represents an example of a steam train made of dice, where the darker dice are the Rule 1: Faces that touch each other have the same number. Rule 2: The number on the top of the funnel must equal the total of the numbers showing on top of the remaining dice that may be seen. Rule 3: You need four or more dice for the train a. If you obey all the rules and use exactly four dice, how many solutions are possible? Clearly explain your process for finding your solutions and how you know that you have found all possible solutions. b. How many solutions are possible if you use exactly five dice? Clearly explain your process for finding your solutions and how you know that you have found all possible solutions. c. You are told that there is a minimum of four dice. Why does that rule make sense? d. Is there a maximum number of dice that you could use for such a train? If so, explain what it is and why that is the maximum possible number. If not, explain why there is no maximum. ote: If you use any mathematical vocabulary, symbols, or operations that have not been covered in class, be ure to define and/or explain them before making use of them.Explanation / Answer
Assumption: The dies have 6 faces
a. If all of the dies are aligned in such a way that they follow the rules then only 3 solutions as otherwise they will not add up to the die values on the top, the maximum value on the die being 6 the solutions are
1,1,1,1
1,1,1,2
1,1,1,3
The sum of all the above figures are less than or equal to 6. Using a combination of any other numbers will give sums greater than 6
b. Again if we use only 5 dies, the only 2 solutions are possible, sum of all figures being less than or equal to 6
1,1,1,1,1
1,1,1,1,2
c. There have to be a minimum of 4 dies as only then the first two rules can be followed in tandem, i.e faces touching each other have the same number and the numbers on top add up to the one on the top of the funnel
d. Yes the maximum number of dies we can use here is 6, as at least one solution that follows all 3 rules will be possible, in that the numbers can add up to the number on the die making up the engine
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