DOMINO HOUSE

The question that we have been given to solve is:

The diagram shows a house built with dominoes. This house has four stories and uses 24 dominoes.

Simon broke the World Record by building a domino house with 73 stories. How many dominoes did he use?

Investigate

To summarise the question about Domino House it is asking you to find how many dominoes are used in n stories to then be able to find out how many dominoes are in 73 stories.

Method

            There are many parts that I will want to include in my project to be able to find the answer and to also allow the reader to understand exactly what I'm doing step by step. I will also explain each section as I work through the investigation.

The sections that I will include in my project are to set out the project and make it simple to understand. Firstly I will use diagrams to make my project easy to understand. I will try to work systematically to make the project simple to understand.

3 dominoes

2 stories

8 dominoes

3 stories

15 dominoes

4 stories

24 dominoes

Results Table

I am now going to record the information I have gathered into a results table, which will allow me to spot any patterns.

In my results table n represents the number of stories and d represents the number of dominoes.

There are two main patterns that I can see here in my results table. The first is that the numbers that are the difference between the number of dominoes are all odd numbers and odd on two each time.

Also, by using the number of stories, and multiply the first story by three and the next by 4 e.t.

            n=  Number of stories.

I am now going to use simultaneous equations to find my rule.

an2+bn+c=d

When n=1        a+b+c=3 (1)

When n=2        4a+2b+c=8 (2)

When n=3        9a+3b+c+15 (3)

Eliminate C

(2)-(1)= 3a+b=5

(3)-(2) = 5a+b=7

Eliminate B

(5)-(4)                         2a=2 therefore a=1

Substitute a=1 into (4)

3+b=5 therefore b=2

 Substitute a=1 and b=2 into (1)

1+2+c=3 Therefore c=0

An2+bn+c=d (dominoes)

1n2(squared)+2n+0=d

n(squared)+2n=d =   RULE

Using the rule that I have just worked out I will now make predictions for a domino house with 5 stories and a domino house, which has 6 stories.

My rule is n(squared)+2n=d

When n=5 5(squared)+(2x5)=d

25+10=35

So a domino house with 5 stories will use 35 dominoes.

When n=6 6(squared)+(2x6)=d

36+12=48

So a domino house with 6 stories will use 48 dominoes.

I am now going to test these predictions by drawing a domino house with 5 stories and a domino house with 6 stories and then count how many dominoes are used to build these domino houses in order to see if my predictions are correct.

Here I can see that this domino house uses 35 dominoes, which means my predictions are correct.

6 Stories.