NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 3: Integers - Problems and SolutionsQuestion 64
Class 6 - Mathematics - Unit 3: Integers - Problems and Solutions
Question. 64
64. Write the digits \(0,1,2,\ldots,9\) in this order and insert '+' or '−' between them to get the result 3.
Answer:
\(0+1+2+3-4+5+6+7-8-9=3\)
Detailed Answer with Explanation:
- Digits from 0 to 9 add up to
(0+1+2+3+4+5+6+7+8+9=45). - When you put some minus signs, you are taking those digits away twice from 45:
Value (=;45-2 imes( ext{sum of digits with }-)). - We want the final value (=3). Set up the equation:
(45-2S=3). - Solve for (S):
(45-3=2S)
(42=2S)
(S=21). - So, the digits that get a minus sign must total (21).
- Pick a simple set that sums to (21):
(9+8+4=21). - Give these digits a minus sign; keep the rest with plus:
(0+1+2+3-4+5+6+7-8-9). - 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).