A-rectangular-cardboard-is-8cm-long-and-6cm-wide-What-is-the-least-number-of-beads-you-can-arrange-on-the-board-such-that-there-are-at-least-two-of-the-beads-that-are-less-than-10-cm-apart-

Question Number 113355 by Aina Samuel Temidayo last updated on 12/Sep/20

A rectangular cardboard is 8 cm long

and 6 cm wide . What is the least

number of beads you can arrange on

the board such that there are at least

two of the beads that are less than

\sqrt{10} cm apart .

Commented by Aina Samuel Temidayo last updated on 12/Sep/20

Solution please ?

Answered by mr W last updated on 13/Sep/20

Commented by mr W last updated on 13/Sep/20

t h e p o i n t s o n t h e g r i d a r e \sqrt{10} a p a r t

f r o m e a c h o t h e r .

w i t h a r e c t a n g l e o f 6 \times 8 w e c a n c o v e r

a t m o s t 9 p o i n t s .

i t m e a n s i f w e p u t 10 p o i n t s o r m o r e

o n t h e 6 \times 8 b o a r d t h e r e a r e a t l e a s t t w o

p o i n t s w h i c h a r e l e s s t h a n \sqrt{10} a p a r t

f r o m e a c h o t h e r .

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