How many artificially made weights are required (minimally) to weigh ONLY 1,3,5,...,79 kg and what should be they?


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Question Number 183664 by Rasheed.Sindhi last updated on 28/Dec/22

$H o w m a n y a r t i f i c i a l l y m a d e w e i g h t s a r e$ $r e q u i r e d (m i n i m a l l y) t o w e i g h$ $\underset{―}{ONLY} 1, 3, 5, . . ., 79 k g$ $a n d w h a t s h o u l d b e t h e y ?$
Commented by Frix last updated on 28/Dec/22

$The problem might be this :$ $If we want to weigh o n l y 1, 3 kg we need$ $∙ 1 and 3 but then we also get 2 and 4$ $∙ 1 and 2 but then we also get 2$ $∙ 1 and 4 but then we also get 4 and 5$ $∙ . 5 and 2.5 . . .$ $\Rightarrow I think {there}^{'} s no solution$
Commented by Rasheed.Sindhi last updated on 29/Dec/22

$T han X Frix sir! v e r y r i g h t a r e y o u . . .$ $I n c a s e w e r e l e a s e t h e \underset{―}{only} c o n d i t i o n$ $h a s t h e q u e s t i o n unique s o l u t i o n$ $You can't use 'macro parameter character #' in math mode$
Commented by mr W last updated on 29/Dec/22

$t o w e i g h o n l y 1, 3, 5, . . ., 79 k g, t h e r e i s$ $n o s o l u t i o n .$ $t o w e i g h n o t o n l y 1, 3, 5, . . ., 79 k g, w e$ $n e e d a t l e a s t 5 w e i g h t s . w i t h 5 w e i g h t s$ $t h e r e a r e a t l e a s t t w o s o l u t i o n s :$ $1, 3, 9, 27, 81 o r$ $1, 2, 6, 18, 54 .$
Commented by Rasheed.Sindhi last updated on 29/Dec/22

$\lor \cap i \subset\in sir! T h a n X!$
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