Lacomus, Damn, No, I mean well done. That answer took me over a week!
I did post the above, above. However, I now see that it would be difficult to make it less clear.
Your reply of 7. Are they all the same size
The full answer. odd number of coins?
Dividing the pennies among the glasses so each glass held an odd number of pennies is impossible. This can be demonstrated with the simple logic that any three odd numbers added together yield an odd number.
The trick, as you probably guessed, was to change the arrangement of the glasses so a penny could be in more than one glass. By placing an even number of pennies into a glass, an odd number of pennies into a second glass, and then placing the second glass into the first, both glasses contain an odd number of pennies.
One example, has two pennies in one glass, three pennies inside a glass within the first glass, and five pennies in the third glass.
Let me put the Beer saga to rest.
"I'll bet $25 I can lift that half full beer bottle one foot off the bar using only this plastic drinking straw. That's right- the only thing I'll touch the bottle with is this straw, and the only thing that will touch the straw other than the bottle will be my hand."
If anyone can get the bottle into the freezer only using the straw, then they win. Otherwise the answer as given is correct in theory and practice, and from what Frank said you will need a lot of practice. :wink:
a = 10
Actually there's nothing wrong with it. Ten does equal 9.99999..., as this proof clearly shows.
Well spotted.
I can give no help with the seven questions. They are reproduced just as I received them. Good luck
Post up the answers as soon as you like. It will give others a chance to comment.