[Guest]

A friend of mine asked me this problem. I haven't yet found the answer to it.

There is a 40 kg weight with a grocerer, he wants to break it into 4 pieces such that he can measure all weights starting from 1 to 40. Can you say which are these four weights ?We have to measure only whole number weights i.e only 1,2, 3....39,40.

[k-man]

Break it into 1,3,9 and 27.

[k-man]

I had some more time, so I put together this table showing how to weigh any whole number of kg between 1 and 40 with just those 4 weights (1kg,3kg,9kg,27kg). The weight to be measured would go on the left side and the weights would go according to this table.

?	Left	Right

1	-	1

2	1	3

3	-	3

4	-	1+3

5	1+3	9

6	3	9

7	3	1+9

8	1	9

9	-	9

10	-	1+9

11	1	3+9

12	-	3+9

13	-	1+3+9

14	1+3+9	27

15	3+9	27

16	3+9	1+27

17	1+9	27

18	9	27

19	9	1+27

20	1+9	3+27

21	9	3+27

22	9	1+3+27

23	1+3	27

24	3	27

25	3	1+27

26	1	27

27	-	27

28	-	1+27

29	1	3+27

30	-	3+27

31	-	1+3+27

32	1+3	9+27

33	3	9+27

34	3	1+9+27

35	1	9+27

36	-	9+27

37	-	1+9+27

38	1	3+9+27

39	-	3+9+27

40	-	1+3+9+27