Friday Riddle
RIDDLE: You die and the devil says he'll let you go to heaven if you beat him in a game. The devil sits you down at a perfectly round table. He gives himself and you an infinite pile of quarters. He says "OK, we'll take turns putting one quarter down, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart and can place quarters perfectly, and you know that if you go first, you can guarantee victory. Explain how you can guarantee victory
Comments

Canadian Quarters?
I realize at once that that 6 quarters will fit in a ring around the outside of the 1st quarter* laid and that each additional ring around will therefore approximate a hexagon with one additional quarter added to each side as it grows. Thus 1st ring  6 quarters; 2nd ring  12 quarters; 3rd ring  18 quarters; 4th ring  24 quarters; etc. etc. etc. Because of the single quarter in the middle the number of quarters to complete a ring will always be an odd number. ie 1,7,13,19,25,31... If I place the 1st quarter I will always be placing an odd number quarter.
I will always complete the circle. I win!
*I know this because the circumference of a circle is larger than its radius by a factor of 6.28 (C=2piR or C=piD) the 1st ring of quarters outside the single quarter can thus fit 6 "diameters" of quarters. Each successively larger ring will increase by a factor of 2pi or 6.28. But since we're dealing with whole quarters... approximately 6.
With Canadian quarters, of course!
I know this is pretty convoluted and am sure there is a more elegant way of saying it! Are you a Math teacher??
Rob; in Vancouver0 
no idea if you are correctrobinvan said:Canadian Quarters?
I realize at once that that 6 quarters will fit in a ring around the outside of the 1st quarter* laid and that each additional ring around will therefore approximate a hexagon with one additional quarter added to each side as it grows. Thus 1st ring  6 quarters; 2nd ring  12 quarters; 3rd ring  18 quarters; 4th ring  24 quarters; etc. etc. etc. Because of the single quarter in the middle the number of quarters to complete a ring will always be an odd number. ie 1,7,13,19,25,31... If I place the 1st quarter I will always be placing an odd number quarter.
I will always complete the circle. I win!
*I know this because the circumference of a circle is larger than its radius by a factor of 6.28 (C=2piR or C=piD) the 1st ring of quarters outside the single quarter can thus fit 6 "diameters" of quarters. Each successively larger ring will increase by a factor of 2pi or 6.28. But since we're dealing with whole quarters... approximately 6.
With Canadian quarters, of course!
I know this is pretty convoluted and am sure there is a more elegant way of saying it! Are you a Math teacher??
Rob; in Vancouver
no idea if you are correct Rob but I vote that YOU WIN!!0 
Quarters packed?robinvan said:Canadian Quarters?
I realize at once that that 6 quarters will fit in a ring around the outside of the 1st quarter* laid and that each additional ring around will therefore approximate a hexagon with one additional quarter added to each side as it grows. Thus 1st ring  6 quarters; 2nd ring  12 quarters; 3rd ring  18 quarters; 4th ring  24 quarters; etc. etc. etc. Because of the single quarter in the middle the number of quarters to complete a ring will always be an odd number. ie 1,7,13,19,25,31... If I place the 1st quarter I will always be placing an odd number quarter.
I will always complete the circle. I win!
*I know this because the circumference of a circle is larger than its radius by a factor of 6.28 (C=2piR or C=piD) the 1st ring of quarters outside the single quarter can thus fit 6 "diameters" of quarters. Each successively larger ring will increase by a factor of 2pi or 6.28. But since we're dealing with whole quarters... approximately 6.
With Canadian quarters, of course!
I know this is pretty convoluted and am sure there is a more elegant way of saying it! Are you a Math teacher??
Rob; in Vancouver
I guess you're placing your quarters as close together as you can, but what if the Devil does not cooperate, and leaves a little extra space around the quarters he puts down? Then, a ring might have an odd number of quarters.
Greg0 
Symmetry.
As Rob says, on your first turn, you put a quarter in the center. If the table is small enough, the game might be over, but if not, wherever the Devil places his quarter, on your next turn, you put a quarter opposite to where the Devil put his. That is, imagining a line drawn through the center of the table and the quarter the Devil just put down, you place your quarter on this line, and just as far from the center quarter as his quarter. Henceforth, after you take your turn, the pattern of quarters will always be symmetrical about the center quarter, because of the strategy you're following. If, after your turn, there is no room for the Devil to add a quarter, of course, you've won. If there is room for him to add a quarter, because of the symmetry of the pattern, there will always be room for you to add a quarter on the opposite side. So, eventually, you will place the last quarter that there is room for.
Greg0 
Yikes...PGLGreg said:Quarters packed?
I guess you're placing your quarters as close together as you can, but what if the Devil does not cooperate, and leaves a little extra space around the quarters he puts down? Then, a ring might have an odd number of quarters.
Greg
I guess I'm looking at a long time in a hot place!!
There's got to be an easier answer to this!
Rob; in Vancouver0 
Wow!PGLGreg said:Symmetry.
As Rob says, on your first turn, you put a quarter in the center. If the table is small enough, the game might be over, but if not, wherever the Devil places his quarter, on your next turn, you put a quarter opposite to where the Devil put his. That is, imagining a line drawn through the center of the table and the quarter the Devil just put down, you place your quarter on this line, and just as far from the center quarter as his quarter. Henceforth, after you take your turn, the pattern of quarters will always be symmetrical about the center quarter, because of the strategy you're following. If, after your turn, there is no room for the Devil to add a quarter, of course, you've won. If there is room for him to add a quarter, because of the symmetry of the pattern, there will always be room for you to add a quarter on the opposite side. So, eventually, you will place the last quarter that there is room for.
Greg
What a cool approach. I like the way you think. Sounds like this works!
Rob; in Van0
Discussion Boards
 All Discussion Boards
 6 CSN Information
 6 Welcome to CSN
 121.6K Cancer specific
 2.8K Anal Cancer
 445 Bladder Cancer
 307 Bone Cancers
 1.6K Brain Cancer
 28.5K Breast Cancer
 395 Childhood Cancers
 27.9K Colorectal Cancer
 4.6K Esophageal Cancer
 1.2K Gynecological Cancers (other than ovarian and uterine)
 13K Head and Neck Cancer
 6.3K Kidney Cancer
 669 Leukemia
 791 Liver Cancer
 4.1K Lung Cancer
 5.1K Lymphoma (Hodgkin and NonHodgkin)
 235 Multiple Myeloma
 7.1K Ovarian Cancer
 57 Pancreatic Cancer
 486 Peritoneal Cancer
 5.4K Prostate Cancer
 1.2K Rare and Other Cancers
 536 Sarcoma
 725 Skin Cancer
 649 Stomach Cancer
 191 Testicular Cancer
 1.5K Thyroid Cancer
 5.8K Uterine/Endometrial Cancer
 6.3K Lifestyle Discussion Boards