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Question Number 74246 by TawaTawa last updated on 20/Nov/19

Answered by MJS last updated on 20/Nov/19

1 2 49  ...  1 25 26  24 triples  2 3 47  ...  2 24 26  22 triples  3 4 45  ...  3 24 25  21 triples    starting with 4: 19  starting with 5: 18  6: 16  7: 15  8: 13  9: 12  10: 10  11: 9  12: 7  13: 6  14: 4  15: 3  16: 1 [16 17 19]    ⇒  200 triples

1249...1252624triples2347...2242622triples3445...3242521triplesstartingwith4:19startingwith5:186:167:158:139:1210:1011:912:713:614:415:316:1[161719]200triples

Commented by mind is power last updated on 21/Nov/19

Nice

Nice

Commented by TawaTawa last updated on 21/Nov/19

God bless your sir

Godblessyoursir

Answered by mind is power last updated on 21/Nov/19

 r+s+t≥3+t⇒t≤49  r+s+t≤t−2+t−1+t⇒t≥((55)/3)⇒t≥19  r+s+t≥1+s+t  ⇒s≤51−t  r+s+t≤s−1+s+t⇒52≤2s−1+t  ⇒s≥((53−t)/2)  ⇒        ((53−t)/2)≤s≤51−t        s≤t−1 ⇒ s≤ min(51−t,t−1)    t−1≥51−t ⇒t≥26  t≥26            ((53−t)/2) ≤s≤51−t  t≤26    ((53−t)/2)≤s≤t−1  Σ_(t=19) ^(26) Σ_(    ((53−t)/2)≤s≤t−1) +Σ_(27) ^(49) Σ_(        ((53−t)/2)≤s≤51−t)   Σ_9 ^(12)  Σ_(26−n≤s≤2n) 1+Σ_(10) ^(13) Σ_(27−n≤s≤2n−1) 1+Σ_(14) ^(24) Σ_(27−n≤s≤51−2n) 1  +Σ_(13) ^(24)     Σ_(26−n≤s≤50−2n)   =Σ_9 ^(12) (3n−25)+Σ_(10) ^(13) (3n−27)+Σ_(14) ^(24) (−n+25)  +Σ_(13) ^(24) (−n+25)  =2+5+8+11+3+6+9+12    =  +2.Σ_(14) ^(24) (−n+25)+12  =(11+1).11+12+56=132+12+56=200

r+s+t3+tt49r+s+tt2+t1+tt553t19r+s+t1+s+ts51tr+s+ts1+s+t522s1+ts53t253t2s51tst1smin(51t,t1)t151tt26t2653t2s51tt2653t2st126t=1953t2st1+492753t2s51t12926ns2n1+131027ns2n11+241427ns512n1+241326ns502n=129(3n25)+1310(3n27)+2414(n+25)+2413(n+25)=2+5+8+11+3+6+9+12=+2.2414(n+25)+12=(11+1).11+12+56=132+12+56=200

Commented by TawaTawa last updated on 21/Nov/19

God bless you sir

Godblessyousir

Commented by mind is power last updated on 21/Nov/19

y′re welcom

yrewelcom

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