There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?<br/>

Let the numbers of 1 kg, 2 kg, 5 kg and 10 kg weights be a,b,c,d respectively.
We need a+2b+5c+10d=20 with a=8,9,10,11.

For a=8: 2b+5c+10d=12 → 3 ways.
For a=9: 2b+5c+10d=11 → 1 way.
For a=10: 2b+5c+10d=10 → 3 ways.
For a=11: 2b+5c+10d=9 → 1 way.

Total ways = 3+1+3+1 = 8.
Hence the maximum number of different ways is 8.