Below is an equation that is not correct yet. By adding a number of plus signs and minus signs between the digits on the left side (without changes the order of the digits), the equation can be made correct.
123456789 = 100
The Question: How many different ways are there to make the equation correct?
One way: 123 - 45 - 67 + 89 = 100. Can you give a systematic way to find answers ?
123 + 45 -67 +89 = 100 1 + 2 - 3 + 4 + 5 + 6 + 78+ 9 = 100
12 + 3 - 4 + 5 + 67 + 89 = 100 1 + 2 + 34 - 5 + 67 - 8 + 9 =100
1 + 23 - 4 +5 +6 +78 -9 = 100 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100
12 -3 - 4 + 5 - 6 + 7 + 89 = 100 12 + 3 4 + 5 -6 - 7 + 89 = 100
1 + 23 - 4 + 56 + 7 + 8 + 9 = 100
Mathexpert:
What is the question?
question is highlighted and underlined.
- 1 + 2 - 3 + 4 + 5 + 6 + 78 + 9 = 100
12 + 3 - 4 + 5 + 67 + 8 + 9 = 100 in the second line above. + is missing between 8 and 9
12 + 3 + 4 + 5 -6 - 7 + 89 = 100 last but one - on the right. + missing betw 3 & 4
Answers
Answered by
39
There are 12 different ways:
123+45-67+8-9 = 100
123+4-5+67-89 = 100
123-45-67+89 = 100
123-4-5-6-7+8-9 = 100
12+3+4+5-6-7+89 = 100
12+3-4+5+67+8+9 = 100
12-3-4+5-6+7+89 = 100
1+23-4+56+7+8+9 = 100
1+23-4+5+6+78-9 = 100
1+2+34-5+67-8+9 = 100
1+2+3-4+5+6+78+9 = 100
-1+2-3+4+5+6+78+9 = 100 (Exceptional, if - sign is allowed to add in front of the first first number).
123+45-67+8-9 = 100
123+4-5+67-89 = 100
123-45-67+89 = 100
123-4-5-6-7+8-9 = 100
12+3+4+5-6-7+89 = 100
12+3-4+5+67+8+9 = 100
12-3-4+5-6+7+89 = 100
1+23-4+56+7+8+9 = 100
1+23-4+5+6+78-9 = 100
1+2+34-5+67-8+9 = 100
1+2+3-4+5+6+78+9 = 100
-1+2-3+4+5+6+78+9 = 100 (Exceptional, if - sign is allowed to add in front of the first first number).
if it was useful please mark as best
lof work done? good
good. u wrote 3 solutions - in addition to what i have written.
how much time did u spend ? actually - do u have a systematic method ?
about 1 hr
Answered by
7
PLS BRAINLEST MARK
123+45-67+8-9=100
123+4-5+67-89=100
123+45-67+89=100
123+4-5-6-7+8-9=100
12+3+4+5-6-7+89=100
12+3+4+5+67+8-19=100
12-3-4+5-6+7+89=100
1+23-4+56+7+8+9=100
1+23-4+5-6+78-9=100
1+2+34-5-67-8+9=100
1+2+3-4+5+6+78+9=100
-1+2-3+4+5+6+78+9=100
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