Grade what is the units digit of the simplest form of ? Answer: Solution

Answer: 26
Solution: The pigeonholes are the grades. Thus, ceiling [N/5] = 6. Therefore, N = 26.

27. 
    100 PIMSO gold medals, 100 PIMSO silver medals and 100 PIMSO bronze medals are placed on a table. How many medals must be selected (randomly) to ensure 3 PIMSO gold medals?
    

Answer: 203
Solution: The worst case scenario is S, S, S, …,S (100), B, B, B,…, B (100), G, G, __. Since only medals are left, then 203 medals must be selected to ensure 3 gold medals.

28. 
    The Philippines is divided into 17 regions: R1, R2, R3, R4A, R4B, R5, CAR, NCR, R6, R7, R8, R9, R10, R11, R12, R13 and BARMM. What is the minimum number of students each of whom comes from one of the 17 regions must participate in PIMSO-Mathematics National Round to guarantee that there are at least 100 students who come from the same region.
    

Answer: 1684
Solution: (17 x 99) + 1 = 1683 + 1 = 1684, since ceiling [1684/17] = 100. Thus, at least 1684 students must participate.

29. 
    SpaceX plans to launch 12,000 Starlink communication satellites on space. However, threats from collision from space debris and other satellites are very likely which could lead to these satellites falling back on earth like a meteorite. Given that the Earth is 70% water and 30% land, how many SpaceX satellite collisions should occur in order for 100 of these SpaceX satellites to hit land and not water?
    

Answer: 8,401
Solution: (12,000)(70%)+1 = 8,401

30. 
    There are 10 PIMSO students in a classroom. It was agreed that all of the students’ cellphones will be put to silent mode and placed on the teacher’s table before the start of the class. When the class is over, everyone picks up a cellphone at random. What is the probability that nobody gets his/her own cellphone?
    

Answer:
Solution: Using the principle of inclusion and exclusion to find the derangement n,






= 1,334,961
Thus, the probability that no student gets his/her own cellphone is
CONGRATULATIONS!
You have reached the end of this challenge. Mabuhay!