Puzzle- Tell the unique weights-Weigh any weight from 1to 40 Kgs

Question: A shopkeeper has four weights for weighing 1 kg to 40 kg. What are these four weights so that he can weigh any weight from 1 kg to 40 kg?

Working on Solution:

Now any normal shopkeeper would following logic:

• 1Kg
• 2Kg
• 5Kg
• 10 Kg weights
  • He can weigh anything from the combination of these…

1,2,3 kgs are straight
4 can be weighed keeping 5kgs on one side and 1kg on another..

6,7,8 are direct combos with 5while 9 is 10 is counter weighed by 1 by another side

10,11,12,13 are straight while 14 is 15 minus 1 on balance

Similarly 16,17,18 are straight

From 19 onwards they will have to weigh one more time to get the number….

Like this any weight can be measured..

“BUT THE MAIN CONDITION IS THAT WEIGHT SHOULD BE USED ONLY ONCE SO THERE HAS TO BE ANOTHER ANSWER “

Correct Answer is :

Right Answer is as follows :
1Kgs
3Kgs
9Kgs
27Kgs weights

These weights are to used only once to wight 1 to 40 Kgs. The combinations of these weights are shown as below:

• 1Kg=1
• 2Kg=3-1
• 3Kg=3
• 4 Kg =3+1
• 5 Kg =9-3-1
• 6 Kg =9-3
• 7 Kg =9-3+1
• 8 Kg =9-1
• 9 Kg =9
• 10 Kg =9+1
• 11 Kg =9+3-1
• 12 Kg =9+3
• 13 Kg =9+3+1
• 14 Kg =27-9-3-1
• 15 Kg =27-9-3
• 16 Kg =27-9-3+1
• 17 Kg =27-9-1
• 18 Kg =27-9
• 19 Kg =27-9+1
• 20 Kg =27-9+3-1
• 21 Kg =27-9+3
• 22 Kg =27-9+3+1
• 23 Kg =27-3-1
• 24 Kg =27-3
• 25 Kg =27-3+1
• 26 Kg =27-1
• 27 Kg =27
• 28 Kg =27+1
• 29 Kg =27+3-1
• 30 Kg =27+3
• 31 Kg =27+3+1
• 32 Kg =27+9-3-1
• 33 Kg =27+9-3
• 34 Kg =27+9-3+1
• 35 Kg =27+9-1
• 36 Kg =27+9
• 37 Kg =27+9+1
• 38 Kg =27+9+3-1
• 39 Kg =27+9+3
• 40 Kg =27+9+3+1