Math Is Fun Forum

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Toothpick problem:

Anyhow I solved this problem:
We connect dots with toothpicks in a grid as shown in Figure 1.14. If there are 10 horizontal toothpicks in each row and 20 vertical ones in each column, how many total toothpicks are there?

The ans says 430 toothpicks, but I my method does not concur, for some peculiar reason.
Here's how I did it: The first row of squares contains 31 toothpicks, additional ones add 21 toothpicks. Since we add 9 more, 21*9=189, so 189+31=220 toothpicks. I feel like I'm missing something crucial, but I can't figure it out currently.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Toothpick problem:

Hi;

I do not understand the question. How do you know how many rows there are? Or how many columns?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Toothpick problem:

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Toothpick problem:

Hi;

I do not understand the question. How do you know how many rows there are? Or how many columns?

---

The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Toothpick problem:

Hi;

I am still not getting it.  I am sorry.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Toothpick problem:

Perhaps I meant- why doesn't my strategy work?

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Toothpick problem:

Hi;

Since I can not visualize this from the diagram you provided I can not answer that.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Toothpick problem:

hi Mathegocart

Your method will work but it's not 31 + 9 x 21 but rather 31 + 19 x 21= 31 + 399 = 430.  There are 19 more rows to add.

bobbym.  This is a grid made up of 10 by 20 squares.  Each square has four 'toothpicks'.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Toothpick problem:

Hi bob bundy;

Thanks!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.