Q-Choose-at-least-some-members-frome-the-set-A-14-15-20-22-23-28-so-that-whith-confidence-includes-three-consecutive-members-

Question Number 209746 by MM42 last updated on 21/Jul/24

Q) C h o o s e a t l e a s t s o m e m e m b e r s

f r o m e t h e s e t A = {14, 15, \dots, 20, 22, 23, \dots, 28}

s o t h a t w h i t h c o n f i d e n c e i n c l u d e s t h r e e c o n s e c u t i v e

m e m b e r s ?

Commented by MM42 last updated on 20/Jul/24

f o r e x a m p l e n = s e l e c t n u m b e r s

n = 3; 14, 15, 16 ✓ o r 14, 15, 17 \times \Rightarrow n o t t r u e

n = 4; 17, 22, 23, 24 ✓ o r 15, 17, 18, 20 \times \Rightarrow n o t t r u e

n = 6; 15, 17, 18, 19, 20, 27 ✓ o r 18, 19, 22, 24, 25, 28 \times \Rightarrow n o t t r u e

m i n (n) = ?; a_{1}, a_{2}, a_{3}, \dots, a_{n}

\Rightarrow \exists 1 < i, j, k < n; a_{k} = a_{j} + 1 = a_{i} + 2

Answered by MM42 last updated on 20/Jul/24

T h e l e a s t n u m b e r o f c h o i c e s c a n b e 11 .

b e c a u s e i n t h e s e t {14, 15, 17, 18, 20, 22, 24, 25, 27, 28} t h e r e a r e n o t h r e e

c o n s e c u t i v e n u m b e r s .

i f w e p u t a n y o t h e r n u m b e r i n t h e s e t, w e w i l l h a v e

t h r e e c o n s e c u t i v e n u m b e r s i n t h e c o l l e c t i o n . ★

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