*OPEN CHALLANGE* सास-याने जावयाला तराजू म्हणजे तागडी दिली.वजनं दिली नाहीत. पूर्ण किलोची चारच वजनं तयार करून आण सांगितले. बारीक खिळ्यांनी भरलेली पिशवी दिली. म्हणाला, "1 ते 31 किलो मधला कोणत्याही पूर्ण किलोचा आकडा सांगितला तरी तितके किलो खिळे मोजून दाखव, सगळी इस्टेट देईन " हुशार जावयाने कोणती चार वजनं बनवलीत ते सांगा तराजूत वजन फक्त एकदाच करायचे आहे. (The Balance is to be used once only )
Answers
Given : To be weighed from 1 to 31 kg using 4 weight
To Find : 4 Weights to weigh all weights from 1 to 31 kg in one weighing only.
Solution:
4 Weights would be
1 , 3 , 9 , 18 ( 18 could have been any number upto 27 ) - 18 is used to get minimum weight
1
3 - 1 = 2
3
3 + 1 = 4
9 - 3 - 1 = 5
9 - 3 = 6
9 - 3 + 1 = 7
9 - 1 = 8
9
9 + 1 = 10
9 - 3 + 1 = 11
9 + 3 = 12
9 + 3 + 1 = 13
18 - 3 - 1 = 14
18 - 3 = 15
18 - 3 + 1 = 16
18 - 1 = 17
18
18 + 1 = 19
18 + 3 - 1 = 20
18 + 3 = 21
18 + 3 + 1 = 22
18 + 9 - 3 - 1 = 23
18 + 9 - 3 = 24
18 + 9 - 3 + 1 = 25
18 + 9 - 1 = 26
18 + 9 = 27
18 + 9 + 1 = 28
18 + 9 + 3 - 1 = 29
18 + 9 + 3 = 30
18 + 9 + 3 + 1 = 31
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