be reals such that 
Prove that 
be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
colors, such that among any 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
This easy via the binomial theorem for the quantity is just 
,
and 
.
Y by
“IMO cheese” is a brand name of processed cheese that comes in a round box containing eight individually wrapped sectors that just fit in the box. Johnny ate two sectors for breakfast, and arranged the remaining ones in the box as shown in the figure. His Mom Pegasus did not like that. She said that Johnny was squeezing the cheese pieces. Johnny insisted that there was no squeezing, the pieces just fit. Who was right?
KöMaL K. 124. (March 2007),G. Kós
KöMaL K. 124. (March 2007),G. Kós
This post has been edited 3 times. Last edited by parmenides51, Mar 25, 2020, 1:02 PM
.
while it's supposed to be at least 
for the sector with the round part touching + 
for the sector with the end touching. But
The cheese pieces were indeed squeezed.
