Hi, coders. I welcome you to Like Shiyan Simulation Round 2. This round will be held on OJ Essential. As usual, you can take any 1h of your spare time.
Hints:
1. Problems: 4 (100-100-50-50)
2. Time: 1h
3. Difficulty: Around Div2D
4. 1 from Atcoder,2 from LOJ,1 from Topcoder(Modified)
5. OI Rule
6. Contest Writer:XGN

Editorial

Problem A - The Lucky Sum

If N>17, the answer is always "YES". How to get this result?
First you need to know that if an integer N can be represented as the lucky sum, N must satisfy the only condition: N=4a+7b (a,b are integers).
Then because gcd(4,7)=1, so the maximum number that cannot be obtained is lcm(4,7)-4-7=17
Source/Extra Topcoder - THELUCKYSUM
Expected Difficulty d2a

Problem B - The Game

Here
Source Atcoder AGC007D
Expected Difficulty d2c for 95%, d2e for AC

Problem C - The Gloves

Here
Source BOI 2008
Expected Difficulty d2c