Originally Posted by

**kowaii**
...teacher said it wold be (x/12) + 1, my only guess is that because we have integer division, we will lose remainder so adding one would ensure we always get more than we need (since it is okay to have left overs)?! is that correct?...

Well, it's "sort of correct" if there is such a thing.

Why don't you do a few manual ('mental") calculations and write down the results.

Forget Java for a minute. Forget about any programming considerations or any stuff about "integer arithmetic." Just think about coffee and coffee pots and cups of coffee.

Interestingly, there was a similar problem in a fifth grade arithmetic book that I saw. It was not about programming. It was about fifth grade arithmetic, and asked questions for a few specific cases. (It was about pizza slices, not cups of coffee, but the principle was the same.)

So...

How many pots will you have to brew if you need zero cups of coffee?

How many pots if you need 5 cups?

11 cups?

12 cups?

13 cups?

.

.

18 cups?

.

.

23 cups?

24 cups?

25 cups?

.

.

.

Now,, spotting a single elegant mathematical expression that gives correct answers for all possible cups requirements might take a little head-scratching. In fact, a single elegant mathematical expression might not be the thing to look for. Just figure out how to get the right answer first.

*Then* try to express it in terms of mathematical operations that can be put into a program.

Anyhow...

First of all, why not write a program that shows results of whatever formula you want to test? Make some kind of loop that lets it calculate the required pot-fillings for various numbers of cups.

I did my own calculations and here's a list that I concocted for zero through 100 cups.

x is the number of cups required from a 12-cup brewing machine.

My
x x/12 x/12+1 Calculation
--------------------------------
0 0 1 0 <---> What's the correct answer here?
1 0 1 1
2 0 1 1
3 0 1 1
4 0 1 1
5 0 1 1
6 0 1 1
7 0 1 1
8 0 1 1
9 0 1 1
10 0 1 1
11 0 1 1
12 1 2 1 <---> What's the correct answer here?
13 1 2 2
14 1 2 2
15 1 2 2
16 1 2 2
17 1 2 2
18 1 2 2
19 1 2 2
20 1 2 2
21 1 2 2
22 1 2 2
23 1 2 2
24 2 3 2 <---> What's the correct answer here?
25 2 3 3
26 2 3 3
27 2 3 3
28 2 3 3
29 2 3 3
30 2 3 3
31 2 3 3
32 2 3 3
33 2 3 3
34 2 3 3
35 2 3 3
36 3 4 3 <---> What's the correct answer here?
37 3 4 4
38 3 4 4
39 3 4 4
40 3 4 4
41 3 4 4
42 3 4 4
43 3 4 4
44 3 4 4
45 3 4 4
46 3 4 4
47 3 4 4
48 4 5 4 <---> What's the correct answer here?
49 4 5 5
50 4 5 5
51 4 5 5
52 4 5 5
53 4 5 5
54 4 5 5
55 4 5 5
56 4 5 5
57 4 5 5
58 4 5 5
59 4 5 5
60 5 6 5 <---> What's the correct answer here?
61 5 6 6
62 5 6 6
63 5 6 6
64 5 6 6
65 5 6 6
66 5 6 6
67 5 6 6
68 5 6 6
69 5 6 6
70 5 6 6
71 5 6 6
72 6 7 6 <---> What's the correct answer here?
73 6 7 7
74 6 7 7
75 6 7 7
76 6 7 7
77 6 7 7
78 6 7 7
79 6 7 7
80 6 7 7
81 6 7 7
82 6 7 7
83 6 7 7
84 7 8 7 <---> What's the correct answer here?
85 7 8 8
86 7 8 8
87 7 8 8
88 7 8 8
89 7 8 8
90 7 8 8
91 7 8 8
92 7 8 8
93 7 8 8
94 7 8 8
95 7 8 8
96 8 9 8 <---> What's the correct answer here?
97 8 9 9
98 8 9 9
99 8 9 9
100 8 9 9

Now, you see that, according to my calculations, x/12 hardly ever gives the correct answer. Also, according to my calculations, x/12+1 is correct more often than not.

However...

For a few values, there is a discrepancy between the teacher's formula and my calculations.

So now some questions arise:

- Do any of the values that I showed disagree with your pencil and paper values? Look at my values and look at your values. Which are correct? If you decide that mine are correct, revisit your calculations and see what could account for the differences. If you decide that yours are correct, show me the steps that allowed you to reach your number.

- Look at the values where my answers disagreed with the teacher's formula. Are my values correct? Are the teacher's values correct?

- Etc.

Cheers!

Z