Five weighing blocks and 121kgs....

Using five weighing blocks how can we weigh any weight up to 121 kgs? What shall be the five weights that have to be considered?

            Because we use a common balance with two compartments it is possible to add as well as reduce weights. If we have 1 kg block 1kg can be weighed. We don’t need a 2kg block because we can measure2kgs by using 3kgs block on one compartment and 1kg weight on the other. It is evident that for weighing 3, 4 kgs we have 1 and 3 kg blocks. Let us see what we will be our next block, blocks 5,6,7,8 are not required, As we add 9 kg block with 1&3  kgs blocks up to 13 kgs can be weighed .As we begin using 1 kg block  1kg is weighed. Here is our little calculation for next block of weight, just 1 more than the two fold.ie, 1*2=2,2+1=3.Using these two blocks up to 4kgs can be weighed. Our next block is 1 more than the double of 4kgs.ie, 9kgs.Using this we can measure up to 13kgs.Next block one more than the double of 13.ie, 13*2=26, 26+1=27.Let us put this in a series form 1, 3,9,27 .We find all of them a multiple of 3.Next number will be 81, very next will be 243.Thus if we have 1,3,9,27,81,243 designations .What is the amount up to which we can make a measurement? To find out, multiply 243 with 3 and reduce 1, ie, 243*3=729,729-1=728.Find the half of the result728/2=364.It can be found that we can measure various weights up to 364 kgs.If we consider 1,3,9,27,81 blocks, 81*3=243,243-1=242,242/2=121.

            We can conclude that a measurement up to 121 kgs can be made with the blocks of 1, 3,9,27 and 81 kgs blocks.