IQ / Programming Quiz (Cannon-Ball Stacks)

[AspDotNetDev]

Answer: [680 (because 120 + 560 equals 680)]

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[Mark_Wallace]

AspDotNetDev wrote:

what would be the minimum number of cannon-balls he could use to make one large tetrahedral pyramid?

A couple of points: - You can't make a tetrahedron with 10 cannon balls; you need 11. - You'd have to define "large".

I wanna be a eunuchs developer! Pass me a bread knife!

[AspDotNetDev]

Mark Wallace wrote:

You can't make a tetrahedron with 10 cannon balls; you need 11.

Since you don't have a picture like I do, I'll give you a hint: 1 + 3 + 6 = 10.

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[AspDotNetDev]

Since you have corrected Mark, I am awarding you "correcting others" points. Good job, me!

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[tolw]

I will throw in the picture[^] :)

[Super Lloyd]

10 ball give a tetrahedron of 3 levels (1 on top, 3 below, 6 below) 20 ball give a tetrahedron if 4 levels (1 on top, 3 below, 6 below, 10 below) just look at tetrahedron of increasing sizes and forecast what was going to happen... [EDIT] each level number of balls = N + previous level (i.e. level N has N(N+1)/2 balls) then you can easily write the table (1, 3, 6, 10, 15, 21, etc...) and play with the numbers...

A train station is where the train stops. A bus station is where the bus stops. On my desk, I have a work station.... _________________________________________________________ My programs never have bugs, they just develop random features.

[AspDotNetDev]

I didn't even have a category for that, but you get points for helping with visuals :)

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[AspDotNetDev]

That is the idea. Easy enough, right? So you should be able to do it, right? Right!? :)

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[Super Lloyd]

Well, didn't I? I think than maybe I didn't understand the question, let me read it again...

A train station is where the train stops. A bus station is where the bus stops. On my desk, I have a work station.... _________________________________________________________ My programs never have bugs, they just develop random features.

[AspDotNetDev]

There is a single numeric answer.

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[Mark_Wallace]

I just made one with mints, and I had to put one in the middle on the third layer. Mind you, the mints are all different sizes and shapes -- but if they were all the same, it would have drained the fun out of it.

I wanna be a eunuchs developer! Pass me a bread knife!

[tolw]

My shot at the answer - quick and not optimized, I'm sure :)

class Program
{
    const int RANGE = 1000;

    static void Main( string\[\] args )
    {
        int sum, p1, p2;
        for( int a = 0; a < RANGE; a++ )
        {
            p1 = ( a \* ( a + 1 ) \* ( a + 2 ) ) / 6;
            for( int b = a + 1; b < RANGE; b++ )
            {
                p2 = ( b \* ( b + 1 ) \* ( b + 2 ) ) / 6;

                for( int i = b + 1; i < RANGE; i++ )
                {
                    sum = ( i \* ( i + 1 ) \* ( i + 2 ) ) / 6;
                    if( sum == p1 + p2 )
                    {
                        Console.WriteLine( sum.ToString() + "=" + p1.ToString() + "+" + p2.ToString() + "\\n" );
                    }
                }
            }
        }
        Console.ReadKey();
    }
}

SPOILER ALERT!! The answer I got is: 680 = 120 + 560 EDIT: I am aware I could have just stopped looking after the first hit - but I was also curious if there would be a lot of results :)

[Andre Kraak]

The number of balls for each level of the pyramid increases like: 1, 3, 6, 10, 15, 21, 28. This means that the number of balls for each larger pyramid is as follows: 4, 10, 20, 35, 56, 84. So we are looking for a pyramid size that can be created with the sizes of the two pyramids that go before it. 84 is the first number for which this is possible, being combined from the pyramids with 35 and 56 balls.

0100000101101110011001000111001011101001

[tolw]

From the OP:

(assuming he uses every cannon-ball in both pyramids)

[AspDotNetDev]

Points awarded for: correctness, elegance, quickness, and mathematical insight. It seems you found an equation for the number of elements in a pyramid for the Nth pyramid. Nice! Since you already have a better program than mine, I might as well share mine now instead of waiting until tomorrow:

public partial class Form1 : Form
{
public Form1()
{
InitializeComponent();
for (var i = 1; i <= 30; i++)
{
txtOut.AppendText(Environment.NewLine + CalculateNumBalls(i).ToString());
}
}

public int CalculateNumBalls(int index)
{
    if (index <= 1)
    {
        return index;
    }
    else
    {
        return CalculateNumBalls(index - 1) + CalculateLayer(index);
    }
}

public int CalculateLayer(int index)
{
    int total = 0;
    for (var i = 1; i <= index; i++)
    {
        total += i;
    }
    return total;
}

}

That just displays the number of balls in the Nth pyramid for the first thirty pyramids. I just used a calculator to see what the difference was between each number. I saved time because I didn't have to calculate all the way down (given largePyramid - mediumPyramid = smallPyramid, I could just stop when smallPyramid was larger than mediumPyramid). Out of curiosity, did you know that formula already, or did you figure it out?

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[AspDotNetDev]

Virtual balls. Also, pool may help. :)

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[Mark_Wallace]

Oh, I know the Maths, but I don't come to the Lounge for work. It's much more fun ignoring thousands of years' learning on triangular numbers, etc, and building pyramids out of mints. I've already done my serious posting of the day. It's a bit much to expect another one.

I wanna be a eunuchs developer! Pass me a bread knife!

[AspDotNetDev]

You keep deleting your messages before I can reply to them, so here is what I was going to say in response to one of them... :)

---

There is no pyramid composed of exactly 91 balls. It goes 84, then 120. You are on the right track though. Let me phrase it another way. There are 3 pyramids: A, B, and C. A is the smallest, B is larger, and C is the largest. The number of balls in C is equal to the sum of the balls in A and B. A does not equal B. This is the question: Find the smallest possible value of C.

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[AspDotNetDev]

If they are thin mints, I fear you may never succeed, as the rate of consumption will outpace the rate of production.

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[AspDotNetDev]

Super Lloyd wrote:

level N has N(N+1)/2 balls

Points for realizing this. I too realized this, but couldn't remember the exact function. :thumbsup:

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