Bags of Dollars

Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

Divide $135 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $135, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require?

Post your answer here!

I'll try to put the answer up May29th!
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

The answer is 8
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

On a train, Smith, Robinson, and Jones are the fireman, brakeman, and the engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smith, a Mr. Robinson, and a Mr. Jones.

1.Mr. Robinson Lives in Detroit.

2.he brakeman lives exactly halfway between Chicago and Detroit

3.Mr. Jones earns exactly $20,000 per year.

4.The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

5.Smith beats the fireman in billiards.

6.The passenger whose name is the same as the brakeman's lives in Chicago.

Who is the Engineer?

I'll put up the answer August 3
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

Catherine is the winner! The answer is Smith.
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

A cylinder 72 cm high has a circumference of 16 cm. A string makes exactly 6 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?
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celtic_girlakp · Posted: Thu Aug 02, 2007 12:33 pm Post subject:

do we post the answer here or in a PM?
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Scott · Senior Member Joined: 18 Feb 2007 Posts: 504

post where everyone can see.
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celtic_girlakp · Posted: Mon Aug 06, 2007 12:39 pm Post subject:

well it may take a while to answer cause I am not good at these math problems.
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

Solution:

The figure alongside illustrates how the cylinder can be unrolled into a rectangle for the case where the string makes exactly 4 complete turns.

For the given problem, the cylinder can be unrolled into a rectangle with dimensions 72 cm by 16 cm. The string thus creates 6 diagonal lines whose measure can be found out by considering the 6 right triangles they can form:

- the base of the triangle is 16 cm and the height is 1/6 of 72 or 12 cm.
- from these, we can get the measure of one diagonal line as 20 cm [i.e., (162 + 122) 1/2] by using the Pythagorean theorem.
- therefore, the whole string measures 120 cm (i.e., 6 x 20 cm
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celtic_girlakp · Posted: Sat Aug 25, 2007 12:12 pm Post subject:

Wow Corteo nicely done. Got another?
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Corteo · Silver Member Joined: 23 Mar 2007 Posts: 138

I think I'll take a small rest.
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celtic_girlakp · Posted: Mon Aug 27, 2007 5:27 pm Post subject:

You go for it. You deserve it!
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