4
Part of 2001 May Olympiad
Problems(2)
10 coins arounc a circle
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L2 P4
9/19/2022
Ten coins of cm radius are placed around a circle as indicated in the figure.
Each coin is tangent to the circle and its two neighboring coins.
Prove that the sum of the areas of the ten coins is twice the area of the circle.
https://cdn.artofproblemsolving.com/attachments/5/e/edf7a7d39d749748f4ae818853cb3f8b2b35b5.gif
geometryareas
set of prime numbers
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L1 P4
9/22/2022
Using only prime numbers, a set is formed with the following conditions:
Any one-digit prime number can be in the set.
For a prime number with more than one digit to be in the set, the number that results from deleting only the first digit and also the number that results from deleting only the last digit must be in the set.
Write, of the sets that meet these conditions, the one with the greatest number of elements.
Justify why there cannot be one with more elements.Remember that the number is not prime.
number theoryprime numbers