For those who love to solve math problems

[AFO]

We wish to weigh our stock; anything between 1 to 40 kilogram.
However, we only are allowed to use 4 different stones to weigh them (the good old-day scales)
For example if you are choosing 1, 2, 3, and 4 kilogram stones then you could (by adding, and deducting) to weigh anything that is 1, 2, 3, 4, 5 (2+3 or 4-1), 6 (2+3+1 or 4+2 or 4+3-1), 7 (4+3), 8 (4+3 +1), 9 (4+3+2), and 10(4+3+2+1).
Now the challenge is to nominate four stones (ONLY 4 STONES) so we could weigh anything between 1-40 kilograms.

The exercise means that you will be able to calculate between 1-40 by using + and _ between 4 numbers.

PS: At each calculation you are allowed to use each number once only (at each given calculation). You may wish not to use all your four numbers/stones but if used one stone/number then you , as I said it earlier only are allowed to used once. You cannot multiply or divide; only + or _. You however can + or _ as many times as you wish as far as you only use each stone/number once at each given calculations. Please refer to above or below examples.

If three of your stones/numbers are 1, 4, and 10 then you could manage to weigh 1, 3, 4, 5, 6, 7, 11, 14, 15, and so forth but of course you cannot calculate or weigh , for example, 36, or 40.

The challenge is to calculate/weigh all numbers (or stones) between 1 to 40 by 4 numbers.

Good luck ladies and gents. Although you need to have a good math problem solving and this has nothing to do with luck!!!

I will post the answer this Monday, unless somone gets it first.

[missIndependent]

ok, herez the smarty Queen, I LOVE MATH..
n i loved this post, but as it is really late overhere, i didnt finished it all lol, heres what i've done so far, of course it might not be right, since i havnt tested evry condition, but i will, maybe tomorrow

4stones: 7, 10, 11, 12 kg

12-11=1
12-10=2
10-7=3
11-7=4
12-7=5
11-(12-7)= 11-5=6 *not sure if it is allowed or not since multiply is kinda forbidden lol
10-(12-7)=10-5=7
12-11+7=8
10+11-12=9
....
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.
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10+11+12+7=40

[missIndependent]

oh, therz no way that my number would work, i cant get 10, n so many others..
it's ok, i'll try again.

[missIndependent]

today's Tuesday
i was accepting the answer yesterday lol














i didnt have time to figure it out, lozza

[AFO]

Sorry, Monday was Memorial Holiday.

1, 3, 9, 27

1=1
2=3-1
3=3
4=3+1

5=9-3-1
6=9-3
7=9-3+1
8=9-1
9=9
10=9+1
11=9+3-1
12=9+3
13=9+3+1

14=27-9-3-1
15=27-9-3
16=27-9-3+1
17=27-9-1
18=27-9
19=27-9+1
20=27-9+3-1
21=27-9+3
22=27-9+3+1
23=27-3-1
24=27-3
25=27-3+1
26=27-1
27=27
28=27+1
29=27+3-1
30=27+3
31=27+3+1
32=27+9-3-1
33=27+9-3
34=27+9-3+1
35=27+9-1
36=27+9
37=27+9+1
38=27+9+3-1
39=27+9+3-1
40=27+93+1

[missIndependent]

smart pants..

thanx for posting the answer, just wanna ask, was there a logic for it, or a quick way to solve it or someone just went over it all n figure it out?