1. ## Walking In Circles

1#
In a perfectly circular arena, I walk from the edge directly to the center. I then turn directly to my left, & walk in a straight line to the edge of the arena. I then turn to the right & follow along the edge for a total of 500 meters until I arrive at the point that I started from. What is the circumference of the inner edge of the arena?

2#
A cube is made of a white material, but the exterior is painted black. If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have 2 of their sides painted black?

3#
Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another).

4#
If you have 3 dice that are shaped as a tetrahedron, a cube, & an icosahedron, & you rolled each of them, each die would display a number from 1-4, 1-6, & 1-20, respectively. Assume that the tetrahedron & icosahedron are regular. If there is an equal chance that a die will display any of its numbers each time it is rolled, what percent chance is there that the numbers rolled will total 7 if all three dice are rolled once, & the numbers they display are added together?

2. ## Re: Walking In Circles

1# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">4/3 * 500 m = 666.67 m</span hide>

3. ## Re: Walking In Circles

2# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">12 * 3 = 36</span hide>

4. ## Re: Walking In Circles

2: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">36</span hide>

5. ## Re: Walking In Circles

I'm going to spike your Pilsner next time... <img src=/S/laugh.gif border=0 alt=laugh width=15 height=15>

6. ## Re: Walking In Circles

3# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">5/3 miles of the fast train, and 1/3 + 2/3 miles of the slow train, making a total of 8/3 = 2.67 miles.</span hide>

7. ## Re: Walking In Circles

3] <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2 miles</span hide>

1# Correct.
2# Incorrect

9. ## Re: Walking In Circles

4# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">14 in 480 or about 2.9 %</span hide>

10. ## Re: Walking In Circles

3# Correct. It would appear that Leif is off form!

Spot on!

12. ## Re: Walking In Circles

If the tunnels are two miles apart, how can there be more than two miles of train protruding from them?

Arrgh! Forget that - I just realised something.... <img src=/S/doh.gif border=0 alt=doh width=15 height=15>

13. ## Re: Walking In Circles

OK - 2: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">44 - if you include cubes with three sides painted black</span hide>

14. ## Re: Walking In Circles

Forget what? <img src=/S/shrug.gif border=0 alt=shrug width=39 height=15>

15. ## Re: Walking In Circles

<img src=/S/thumbup.gif border=0 alt=thumbup width=15 height=15>

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