Get a total 900

You have the nine distinct digits 1,2,3,4,5,6,7,8 and 9.You are allowed to form 3 numbers each of 3 digits from these,without using any digit more than once..The requirement is that the total of these 3 numbers should be 900.Try forming the numbers.

Two sets of five digits each

I had dealt with earlier 2 sets of five distinct digits each,where the numbers formed from the first,could be double the numbers you can form from the second-examples below-
76902(38451)....96702(48351).....69702(34851).....etc etc
You can similarly have sets where numbers from the first could be triple or one-third the numbers from the second-Examples below-
50382(16794)......53082(17694)......20583(61749)
Can you find more such cases?

using a set of scales fornweighment-rejoinder-2

In case the weights are placed on only one side of the scales,the weight of the item being weighed will be the total of the weights placed on that side.If the weights are placed on both sides,the weight will be the sum of weights placed on opposite side less the sum of weights placed by the side of the item.
You will be surprised the weights required will be the numbers formed by repeatedly multiplying 1 with 3,viz 1,3,9,27,81,243,729 ......etc
Thus if the item weighs 60 gm,you will have to work out how you can get 60 by adding or subtracting those numbers.You will find 60=81-27+9-3.Thus weights 27 and 3 are placed by the side of the item weighed and 81 and 9 placed on the opposite side.
Similarly for any item weighed.
For item weighig 301 gm,you will find 301=243+81-27+3+1.So you  have to place weight 27 by the side side of the item weighed and all others on the opposite side.
Try finding what and how the weights are to be placed for items weighing 400 and 368.A tricky exercise.

Using a set of scales for weighment-rejoinder

I have not received any response to my earlier blog-The same related to the minimum number of weights required to weigh materials with weights upto 80 kg using a set of scales.
The procedure is based on the property relating to numbers formed by repeatedly multiplying 1 wth 2.
The numbers are 1,2,4,8,16,32,64,128,256   etc etc
These numbers could be added to each other without repetitions to produce any total you require and thus these will be values of the weights required for weighig any material
If you use 1,2,4,8,16 you could weigh upto 31kg
If you use 1,2,4,8,16,32 you could weigh upto 63 kg
If you use 1 2 4,8,16,32,64,you could weigh upto 127 kg and so on
For example the weighment of an item with weight  115 kg will require the weights 64,32,16,2 and 1
Similarly for 105 kg,you will require  the weights 64,32,8 and 1 and so on
Let me put a question now.Suppose you are allowed to place weights on both sides of the scales.What will be weights needed? 

Walk the talk

I got a comment recently that my numbers have not walked for some recent time past.I am now showing they could walk the talk also.This is an imaginary conversation between numbers 2 and 5.
The younger member Y(2)started the talk.
Hello can we become friends?
Elder member E(5) replied.
Dont you know .we are already friends ,whenever I regenerate myself you are close by my side like in 5*5=25 and 25*5=625 etc.Also when I regenerate myself 5 times I become yourself in disguise..Check it 5*5*5*5*5=3125...3+1+2+5=11...1+1=2
Similarly when you regenerate yourself 5 times,you become myself in disguise....Check it.2*2*2*2*2=32...3+2=5
 I will reveal to you more about our friendship in our next conversation.

Using a set of scales for weighment

Suppose you have a set of scales useful for weighing any article.Suppose also that you are allowed to place the article on one side.and that weights are allowed to be placed only on the other side.Suppose you are required to weigh articles upto  80 kg.The question is what is the minimum number of weights required to weigh any article where they can weigh from 1kg upto 80 kg.I will wait for a response before giving the answer.

Divide by 12 to get a remainder.

Take any prime number like 19.
Square it and add 14.You will get 361+14=375
Now divide by 12,you get 3 as reminder.
Even if you take any other prime number and work similarly,you will get the same remainder.
If you add 17 instead of 14,you will always get 6 as the remainder.
Even if you take any odd number not divisible by 3 instead of any prime number,you will have similar results..

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