Puzzle: This is part 2 of puzzle posted yesterday. The puzzle is that you have to weigh 1 to 1000 using a common balance scale with minimum number of weighs. This time you can put wights on both sides.
You can check Part 1 of this puzzle How many weights? Puzzle Part 1.
Note: Don't forget to visit us again. Answer to the puzzle will be posted tomorrow with winner's name. You can provide your answer in comments.
Solution: The answer is series of base 3 i.e. 1, 3, 9, 27, 81, 243 and 729.
We can start from smallest number 1. To measure 1 we definitely need 1.
To measure 2 we need to look for highest number possible. We can measure 2 by using 3(3-1 = 2). So we need 1 and 3.
Now to measure 4 we can use 1 and 3 both (1+ 3). To measure 5 again we will look for highest possible number. 9 is highest possible number (9-4 = 5). We can measure up to 13 using these weights.
Continuing the same way we can deduce that a series of base 3 is required, thus 1, 3, 9, 27, 81, 243, 729.
Winner: Kasturi wins again with her excellent explanation.
Lets start from 1. We need the number 1 in any case. Whenever you cannot calculate a number from the already present ones, try to include the largest number you can.
ReplyDeleteI cannot calculate 2 from 1. The largest number I can include that will allow me to calculate 2 is 3 (2=3-1). (Which I get by adding twice of the last included number i.e. 1+1*2)
Now I have 1,3.
From them I can calculate upto 4. To get 5, again the largest number I can include is by adding twice the last included number which is 3+3*2=9. (5=9-(3+1))
Now, I have 1,3,9.
From them, I can calculate upto 13. To calculate 14, the largest number I can include is by adding twice the last included number which is 9+9*2=27. (14=27-(9+3+1))
Now, we have 1,3,9,27.
If we see the pattern, everytime, we are adding twice the last number which essentially multiplies the last number by 3.
Hence, to calculate upto 1000, we need 1,3,9,27,81,243 and 729 i.e. 7 weights.
how are u measuring other number like 7 11..can u atleast show me upto 13 number ..i means as we can put 2 weight now what weight we are putting & when ..e.g how we are measuring the
ReplyDelete