Puzzle -If you are good in maths

[Qoo]

Indeed, 1,3,9,27 doesn't work in any except the A+B+C+D=40kg.

[pankaj]

Well, this will explain is better.

Google helped me to find out the exact meaning of the question and the solution mentioned here will make the question even clear.

Q. A 40 Kg weight measure broke into 4 pieces in such a way that ,by using one or combinations of them in one or two trays of a balance all weighings could be done from 1 to 40 (no fraction) Please find out the weight of each broken piece.

OR

Q. A boy had a bar of lead that weighed 40 pounds, and he divided it into 4 pieces in such a way as to allow him to weigh any number of pounds from 1 to 40. How did he manage the matter?


SOLUTION

Divide the 40-pound bar into sections of 1, 3, 9, and 27 pounds. Using a two-sided balance scale, place the object to be weighed on the left side. Then place the “added” weights on the right side, and the “subtracted” weights on the left side; if the scale is balanced in the following combinations, then the left-side value is the weight of the object being weighed.
40 = 27 + 9 + 3 + 1 (i. e., if all four weights are on the right side while the object is on the left side of the scale and it is balanced, then the object weighs 40 pounds)
39 = 27 + 9 + 3
38 = 27 + 9 + 3 – 1
37 = 27 + 9 + 1
36 = 27 + 9
35 = 27 + 9 – 1
34 = 27 + 9 – 3 + 1
33 = 27 + 9 – 3
32 = 27 + 9 – 3 – 1
31 = 27 + 3 + 1
30 = 27 + 3
29 = 27 + 3 – 1
28 = 27 + 1
27 = 27
26 = 27 – 1
25 = 27 – 3 + 1
24 = 27 – 3
23 = 27 – 3 – 1
22 = 27 – 9 + 3 + 1
21 = 27 – 9 + 3
20 = 27 – 9 + 3 – 1
19 = 27 – 9 + 1
18 = 27 – 9
17 = 27 – 9 – 1
16 = 27 – 9 – 3 + 1
15 = 27 – 9 – 3
14 = 27 – 9 – 3 – 1
13 = 9 + 3 + 1
12 = 9 + 3
11 = 9 + 3 – 1
10 = 9 + 1
9 = 9
8 = 9 – 1
7 = 9 – 3 + 1
6 = 9 – 3
5 = 9 – 3 – 1
4 = 3 + 1
3 = 3
2 = 3 – 1
1 = 1

How to get the numbers {1 3 9 27}:

The maximum distance between weights must be observed to fill in all the ‘gaps,’ with the smaller weights closer together and the larger weights increasingly far apart. In other words, figure out the smallest units first, then the greatest combination they can reach with all the ‘gaps’ filled in; the difference between the next unknown number minus the sum of the known numbers will be one greater than the sum of the known numbers.

a must = 1, or else the weight 39 could not be achieved.
b – a = 2; therefore b = 3.
since a + b = 4, c – (a + b) = 5, therefore c = 9.
All combinations smaller than a + b + c can now be reached; a + b + c = 13. Therefore d – (a + b + c) must = 14, so d = 27.

Source - http://www.smart-kit.com/s764/bar-of-lead/

[Hime]

Well, this will explain is better.

Google helped me to find out the exact meaning of the question and the solution mentioned here will make the question even clear.

Q. A 40 Kg weight measure broke into 4 pieces in such a way that ,by using one or combinations of them in one or two trays of a balance all weighings could be done from 1 to 40 (no fraction) Please find out the weight of each broken piece.

OR

Q. A boy had a bar of lead that weighed 40 pounds, and he divided it into 4 pieces in such a way as to allow him to weigh any number of pounds from 1 to 40. How did he manage the matter?


SOLUTION





Source - http://www.smart-kit.com/s764/bar-of-lead/

Well...indeed...but then the given conditions are useless Whoever tried those conditions made a wrong conclusion(which are not wrong mathematically though).

[pankaj]

Yeah, right. I myself failed to understand the question.

I guess Nitish might have searched it via Google because its really very difficult to understand the question in the manner it was explained.

[foxman]

WTF is this? I am going crazy with these stones!

[St0neF!sh]

LOL!.... If all of you guys didn't understand the question, why don't you ask for more explanation before Nitish replied...

Learn more, before saying "Question is out of Syllabus!"