NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 3: Integers - Problems and Solutions

Question 64

1. Digits from 0 to 9 add up to
   (0+1+2+3+4+5+6+7+8+9=45).
2. When you put some minus signs, you are taking those digits away twice from 45:
   Value (=;45-2 imes( ext{sum of digits with }-)).
3. We want the final value (=3). Set up the equation:
   (45-2S=3).
4. Solve for (S):
   (45-3=2S)
   (42=2S)
   (S=21).
5. So, the digits that get a minus sign must total (21).
6. Pick a simple set that sums to (21):
   (9+8+4=21).
7. Give these digits a minus sign; keep the rest with plus:
   (0+1+2+3-4+5+6+7-8-9).
8. Quick check (run through left to right):
   (0+1=1)
   (1+2=3)
   (3+3=6)
   (6-4=2)
   (2+5=7)
   (7+6=13)
   (13+7=20)
   (20-8=12)
   (12-9=3).

Answer used: (0+1+2+3-4+5+6+7-8-9=3).