# Mathematics

### #21

Posted 27 September 2001 - 05:10 PM

The following multiplication example uses all the digits from 0 to 9 once and once only (not counting the intermediate steps). Finish the problem. One number has been filled in to get you started.

xxx

x5

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xxxxx

### #22

Posted 27 September 2001 - 05:13 PM

There are two lengths of rope.

Each one can burn in exactly one hour.

They are not necessarily of the same length or width as each other. They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

### #23

Posted 27 September 2001 - 06:47 PM

Khelatsi em

### #24

Posted 29 September 2001 - 11:23 AM

but wait at least couple of days before giving the answers, please.

### #25

Posted 29 September 2001 - 12:08 AM

Originally posted by Azat:

**2. You have fifty bags, each with approximately one hundred balls inside. You have a weighing machine with a digital readout, with 3 places of decimals on the display, calibrated in grams, it is capable of weighing an infinite amount (but it won't have to). All of the balls in all of the bags weigh 1 gram, except in one bag in which all of the balls weigh 1.001 grams. You cannot tell by look or feel which bag has the heavier balls.**

How do you determine which bag contains the heavier balls?

You can use the weighing machine only once (which means you can obtain only one reading from it before it self destructs).

How do you determine which bag contains the heavier balls?

You can use the weighing machine only once (which means you can obtain only one reading from it before it self destructs).

Ok. i think i got this one. here it is.

===

first you number all of the bags from 1 to 50.

then you take 1 ball from bag #1, 2 balls from bag #2, 3 from #3, and so on.

you put all of those balls together and wight them.

then you look to the result.

if it says (i don't want to calculate so i'll use *s) ****.001 then #1 bag is the one with heavier balls

if it says ****.002 then it's #2.

****.003 then it's #3.

and so on.

and THEN you hide so you won't be hurt from the destruction. but be sure to read what it says first. even if you have to take high risk

=====

this one was easy. but the rest will take a while.

### #26

Posted 29 September 2001 - 02:03 AM

In how many ways can you measure the height of a tall building with a thermometer? (I'll try to remember all the answers - I think there were six of'em!)

(Hint: be silly.)

### #27

Posted 29 September 2001 - 09:24 AM

Originally posted by Thorny Rose:

**I'll bring this one in myself:**

In how many ways can you measure the height of a tall building with a thermometer? (I'll try to remember all the answers - I think there were six of'em!)

(Hint: be silly.)

In how many ways can you measure the height of a tall building with a thermometer? (I'll try to remember all the answers - I think there were six of'em!)

(Hint: be silly.)

Offer the janitor a thermometer in exchange for the height of the building.

### #28

Posted 29 September 2001 - 09:30 AM

Originally posted by wh00t:

Offer the janitor a thermometer in exchange for the height of the building.

Offer the janitor a thermometer in exchange for the height of the building.

Erm, no... I had some more creative stuff on my mind.

I know it's not about math, but... Maybe we might come up with more than six or so ways and exchange some funny stuff...

### #29

Posted 29 September 2001 - 03:23 PM

Originally posted by Harut:

Ok. i think i got this one. here it is.

===

first you number all of the bags from 1 to 50.

then you take 1 ball from bag #1, 2 balls from bag #2, 3 from #3, and so on.

you put all of those balls together and wight them.

then you look to the result.

if it says (i don't want to calculate so i'll use *s) ****.001 then #1 bag is the one with heavier balls

if it says ****.002 then it's #2.

****.003 then it's #3.

and so on.

and THEN you hide so you won't be hurt from the destruction. but be sure to read what it says first. even if you have to take high risk

=====

this one was easy. but the rest will take a while.

Ok. i think i got this one. here it is.

===

first you number all of the bags from 1 to 50.

then you take 1 ball from bag #1, 2 balls from bag #2, 3 from #3, and so on.

you put all of those balls together and wight them.

then you look to the result.

if it says (i don't want to calculate so i'll use *s) ****.001 then #1 bag is the one with heavier balls

if it says ****.002 then it's #2.

****.003 then it's #3.

and so on.

and THEN you hide so you won't be hurt from the destruction. but be sure to read what it says first. even if you have to take high risk

=====

this one was easy. but the rest will take a while.

Very good Harut.

I thought this was the hardest and the others are just tricky.

I have few more in my old emails. My friend and I use to email each other these type of problems long time ago. Now I need to go and dig them out.

### #30

Posted 29 September 2001 - 03:33 PM

Originally posted by Thorny Rose:

**I'll bring this one in myself:**

In how many ways can you measure the height of a tall building with a thermometer? (I'll try to remember all the answers - I think there were six of'em!)

(Hint: be silly.)

In how many ways can you measure the height of a tall building with a thermometer? (I'll try to remember all the answers - I think there were six of'em!)

(Hint: be silly.)

Hey Thorny, good question.

Lets see.

1. Can you go to the top and measure the temperature and measure the temperature at the bottom and figure out the height because the temperature goes down X degrees for each Y meters?

2. You can possibly boil water on top of the roof and measure the temperature of the water at the boiling point. Water boils at lower temperature at higher altitude and based on the boiling point you can determine the height.

3. Drop the thermometer from the roof and measure the time it takes for it to hit the ground and based on the time and theory of acceleration you can get the height.

Okay, I have to admit, I have no clue. I need some hints.

### #31

Posted 30 September 2001 - 02:38 PM

Today I am going to be a cheap home owner(I am playing myself)

I am going to hire you two to plant 5 rows of trees for me. 4 trees per row. But remember I am cheep so I can only afford to buy 10 trees.

How are you guys going to plant the 10 trees such that it is 5 rows of 4 trees each.

Hey Thorny, I am still waiting for your hints on the height of the building.

Azat

### #32

Posted 30 September 2001 - 03:02 PM

If you draw this grid, the square in the upper left-hand corner we could say is one, and the one next to it is two, three, four, five, and then the line below that is six, seven, eight, nine, 10, 11, 12... All the way to 25.

Now put a person in each square. You have to move each person from the square they are into the square of one of his adjacent squares. So number one can move to square number two, or number six, for example.

Number two can move to number one. Or number three, or number seven.

So, here's the question. What is the fewest number of total moves that will allow every person to move to an adjacent square?

### #33

Posted 30 September 2001 - 06:27 PM

Monday morning Jack plants a magic bean. When Jack waters the plant on Tuesday morning it has grown to a height of 4ft. When Jack waters the plant on Wednesday moring it is 6ft tall. When Jack waters the plant on Thursday morning it is 7ft tall.

If Jack's magic plant continues to grow at the same rate, how many days will it take Jack's magic plant to grow to a height of 8ft?

[ September 30, 2001: Message edited by: Armo ]

### #34

Posted 30 September 2001 - 06:40 PM

Originally posted by Armo:

**Here's a problem you guys can also try..it's called the Magic Plant.**

Monday morning Jack plants a magic bean. When Jack waters the plant on Tuesday morning it has grown to a height of 4ft. When Jack waters the plant on Wednesday moring it is 6ft tall. When Jack waters the plant on Thursday morning it is 7ft tall.

If Jack's magic plant continues to grow at the same rate, how many days will it take Jack's magic plant to grow to a height of 8ft?

[ September 30, 2001: Message edited by: Armo ]

Monday morning Jack plants a magic bean. When Jack waters the plant on Tuesday morning it has grown to a height of 4ft. When Jack waters the plant on Wednesday moring it is 6ft tall. When Jack waters the plant on Thursday morning it is 7ft tall.

If Jack's magic plant continues to grow at the same rate, how many days will it take Jack's magic plant to grow to a height of 8ft?

[ September 30, 2001: Message edited by: Armo ]

Armo jan, inchkan el jres meka 8 fti chi hasni.

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it won't be 8 ft tall ever.

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i can now see that you are studying calculas.

### #35

Posted 30 September 2001 - 07:08 PM

Originally posted by Azat:

**Okay Harut and Thorny,**

Today I am going to be a cheap home owner(I am playing myself)

I am going to hire you two to plant 5 rows of trees for me. 4 trees per row. But remember I am cheep so I can only afford to buy 10 trees.

How are you guys going to plant the 10 trees such that it is 5 rows of 4 trees each.

Hey Thorny, I am still waiting for your hints on the height of the building.

Azat

Today I am going to be a cheap home owner(I am playing myself)

I am going to hire you two to plant 5 rows of trees for me. 4 trees per row. But remember I am cheep so I can only afford to buy 10 trees.

How are you guys going to plant the 10 trees such that it is 5 rows of 4 trees each.

Hey Thorny, I am still waiting for your hints on the height of the building.

Azat

i don't know how Thorny wants to do it, but i'll plant them it STAR shape.

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i think you can see 5 lines

### #36

Posted 30 September 2001 - 09:46 PM

Originally posted by Harut:

i don't know how Thorny wants to do it, but i'll plant them it STAR shape.

^^^^^^*^^^^^^^

^^*^^*^*^^*^^^

^^^^*^^^*^^^^^

^^^^^^*^^^^^^^

^^^*^^^^^*^^^^

i think you can see 5 lines

i don't know how Thorny wants to do it, but i'll plant them it STAR shape.

^^^^^^*^^^^^^^

^^*^^*^*^^*^^^

^^^^*^^^*^^^^^

^^^^^^*^^^^^^^

^^^*^^^^^*^^^^

i think you can see 5 lines

You're hired. I just hope you don't charge too much money.

### #37

Posted 30 September 2001 - 10:28 PM

Originally posted by Azat:

**Good.**

Here are 2 more

1. Two strangers from different parts of America both build similar apartment buildings in their home towns. By chance, they both forget an important part of their project. They each, once again by chance, call the same national hardware store and order the missing items. The prices they are quoted are as follows:

one will cost them $2.

two will cost them $2.

twelve will cost them $4.

and a hundred and forty-four will cost $6.

What was the item they needed?

Here are 2 more

1. Two strangers from different parts of America both build similar apartment buildings in their home towns. By chance, they both forget an important part of their project. They each, once again by chance, call the same national hardware store and order the missing items. The prices they are quoted are as follows:

one will cost them $2.

two will cost them $2.

twelve will cost them $4.

and a hundred and forty-four will cost $6.

What was the item they needed?

Azat jan, bayts du shat shustri es.

et inchi tverov cheir grel?

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i got this one too.

the items they needed are the numbers for the doors

1 is $2

2 is $2

12 is $4

144 is $6

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i liked this one, Azat.

### #38

Posted 30 September 2001 - 10:33 PM

Originally posted by Azat:

You're hired. I just hope you don't charge too much money.

You're hired. I just hope you don't charge too much money.

no, at all. i offer very cheap labor.

let's see. one tree costs $20.

you need 5 rows, 4 tree on each. that would be $400.

### #39

Posted 01 October 2001 - 11:56 AM

Originally posted by Harut:

Azat jan, bayts du shat shustri es.

et inchi tverov cheir grel?

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i got this one too.

the items they needed are the numbers for the doors

1 is $2

2 is $2

12 is $4

144 is $6

------

i liked this one, Azat.

Azat jan, bayts du shat shustri es.

et inchi tverov cheir grel?

----

i got this one too.

the items they needed are the numbers for the doors

1 is $2

2 is $2

12 is $4

144 is $6

------

i liked this one, Azat.

Harut jan, I am impressed. What is it you study? Your logic is great.

What is it you study?

### #40

Posted 01 October 2001 - 12:10 AM

I am sure this is going to be easy for you as well.

Remember the balls from the previous question? You take 1 ball from each bag and mix them. Such that 49 are the same weight and 1 is just a little heavier. Now you have a have to find which one is the heavy ball with my balance scale.

You only have 5 dollars and I charge a dollar each time you use the balance scale(to pay the tree gardener ). How do you find the heavy ball? To make it harder for you. You also want to buy Thorny ice cream and that costs a dollar. How can you do both? Buy the ice cream and find the heavy ball?

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