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Weighty Problem: Solution
My friend should get the following four weights: 1 kg, 3 kg, 9 kg and 27 kg. This will allow him to measure all whole kilograms up to 40 kg.
This is how he will go about it:
1 kg: He already has 1 kg.
2 kg: He places 3 kg on one side of the balance and 1 kg on the other side. Thus, 2 kg = 3 kg - 1 kg.
3 kg: He already has 3 kg.
4 kg: 3 kg + 1 kg.
5 kg: 9 kg - (3 kg + 1 kg). So, he places 9 kg on one side of the balance, and 3 kg and 1 kg weights on the other side.
6 kg: 9 kg - 3 kg.
7 kg: (9 kg + 1 kg) - 3 kg.
8 kg: 9 kg - 1 kg
9 kg: He already has 9 kg.
10 kg: 9 kg + 1 kg.
11 kg: (9 kg + 3 kg) - 1 kg.
12 kg: 9 kg + 3 kg.
13 kg: 9 kg + 3 kg + 1 kg.
14 kg: 27 kg - (9 kg + 3 kg + 1 kg).
15 kg: 27 kg - (9 kg + 3 kg).
16 kg: (27 kg + 1 kg) - (9 kg + 3 kg).
17 kg: 27 kg - (9 kg + 1 kg).
18 kg: 27 kg - 9 kg.
19 kg: (27 kg + 1 kg) - 9 kg.
20 kg: (27 kg + 3 kg) - (9 kg + 1 kg).
21 kg: (27 kg + 3 kg) - 9 kg.
22 kg: (27 kg + 3 kg + 1 kg) - 9 kg.
23 kg: 27 kg - (3 kg + 1 kg).
24 kg: 27 kg - 3 kg.
25 kg: (27 kg + 1 kg) - 3 kg.
26 kg: 27 kg - 1 kg.
27 kg: He already has 27 kg.
28 kg: 27 kg + 1 kg.
29 kg: (27 kg + 3 kg) - 1 kg.
30 kg: 27 kg + 3 kg.
31 kg: 27 kg + 3 kg + 1 kg.
32 kg: (27 kg + 9 kg) - (3 kg + 1 kg).
33 kg: (27 kg + 9 kg) - 3 kg.
34 kg: (27 kg + 9 kg + 1 kg) - 3 kg.
35 kg: (27 kg + 9 kg) - 1 kg.
36 kg: 27 kg + 9 kg.
37 kg: 27 kg + 9 kg + 1 kg.
38 kg: (27 kg + 9 kg + 3 kg) - 1 kg.
39 kg: 27 kg + 9 kg + 3 kg.
40 kg: 27 kg + 9 kg + 3 kg + 1 kg.
Some useful links for
your career:
- Union Public Service Commission - www.upsc.gov.in
- IIT-Kharagpur - www.iitkgp.ac.in
- Indian Statistical Institute - www.isical.ac.in
- Indian Institute of Technology Madras - www.iitm.ac.in
- Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
- Indian Institute of Mass Communication - www.iimc.nic.in
- IIT Bombay - www.iitb.ac.in
- Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
- Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
- Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
- Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
- Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
- Tata Institute of Social Sciences, Mumbai - www.tiss.edu