Five-minute 80951

Karel has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one.

Correct answer:

z = 22*1+3*2
z2 = 23*1+1*2+1*3

Step-by-step explanation:

μ=1.12 n=22  μ2=n+1n 1+2=22+122 1+2=2324=12311.0435 μ3=n+1n 1+3=22+122 1+3=2325=12321.087 μ4=n+1n 1+4=22+122 1+4=2326=12331.1304 μ5=n+1n 1+5=22+122 1+5=2327=12341.1739  μ4>μ; μ5>μ  μ (n+x)=n 1+x 2 1.12 (22+x)=22 1+x 2  0.88x=2.64  x=0.882.64=3  x=3  z=22 1+3 2
1.12=a+b+c1 a+2 b+3 c 112 (a+b+c) = 100 (1 a+2 b+3 c) 112a+112b+112c = 100a+200b+300c 12a = 88b+188c 3a = 22b+47c;a>0;b  0;c  0  a1=22,b1=3,c1=0 a2=23,b2=1,c2=1 a3=44,b3=6,c3=0 a4=45,b4=4,c4=1 a5=46,b5=2,c5=2 a6=47,b6=0,c6=3 a7=66,b7=9,c7=0 a8=67,b8=7,c8=1 a9=68,b9=5,c9=2 a10=69,b10=3,c10=3 a11=70,b11=1,c11=4 a12=88,b12=12,c12=0 a13=89,b13=10,c13=1 a14=90,b14=8,c14=2 a15=91,b15=6,c15=3 a16=92,b16=4,c16=4 a17=93,b17=2,c17=5 a18=94,b18=0,c18=6 a19=110,b19=15,c19=0   z2=23 1+1 2+1 3

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