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.