36 of 100: Add Seven Subtract One

Let $x$ be the number with the subtraction sign in front of it.

Let all the " $\square$ "s contain the additional sign.

As the result, the equation becomes,

$1+2+3+4+5+6+7+8=30+2x$

$36=30+2x$

$2x=6$

$x=3$

Therefore, the subtraction sign is between the 2 and 3.

Solution to this problem? Don't trust your intuition!

Applying n(n+1)/2 formula, the sum of 1+2+3+4+5+6+7+8 = 36.

The sum stands 30 without 6. If you subtract 6 instead of adding it, the result would be 24.

Subtracting 3 we get the result- 30.

Answer: Between the 2 and 3

The sum of all numbers is $1+2+3+4+5+6+7+8=36$ . Subtract $6$ from both sides to get $1+2+3+4+5+6+7+8-6=36-6=30$ , but $3-6=-3$ , so $1+2-3+4+5+6+7+8=30$ , then the minus sign goes between 2 and 3.

The trick with this problem is to realize that by putting substraction sign before some number, you don't just substract that number, but also repeal addition of that number!

The analogy is similar with having coins in your pockets: moving some amount of coins from one pocket to another will not only increase the number of coins in the second pocket, but also decrease number of coins in the first pocket. Let we say that in the left pocket we have 36 coins (which correspond to left side of the equation) and that in the right pocket we have 30 coins (which correspond to right side of the equation). The question now becomes: how many coins we need to move from our left to our right pocket so that we have equal number of coins in both of them? The answer is, of course, $3$ !

The answer must be ''Between 2 and 3.''

Because,

$\Rightarrow 1 + 2 - 3 + 4 + 5 + 6 + 7 + 8 = 30$

Another way,

$\Rightarrow 0 + 4 = 4 + 5 = 9 \implies 9 + 6 = 15 + 7 = 22 \implies 22 + 8 =$ $30$

Therefore, if subtraction sign go to 'Between 2 an 3' $,$ the equation will be true.

1+ 2+ 3+ 4+ 5+ 6+7 +8 =36

so , by subtracting 6, it will be= 1+ 2+3 +4+ 5 -6 +7 +8=24........................[cz, if we subtract 6 it is already (36-6) =30 and subtracting result is 30-6=24]

so, if we subtract 3, it will be=1+2-3+4+5+6+7+8=30.....................[CZ, IF WE SUBTRACT 3 it is already 36-3=33 and the subtracting result is 33-3=30]

so,it will be between 2 & 3

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By placing it between 1-2, it results in 28. By placing it in between 2 and 3, it results as 30.

1+2-3+4+5+6+7+8=30 First, 1+2=3 ,then 3-3=0 Finally, 0+4+5+6+7+8=30

The sum of all 8 numbers will be: (n/2)*(a1+ an) = 4 * 9 = 36

Let the missing bum to substract be x. So if we need the sum of all the 7 other numbers the sum will be: 36 - x. We need to substract again the same number, so our equation will be: 36 - 2x = 30 And x = 3, that's why we substract 3.

1+2+3+4+5+6+7+8= 36

1+2+3+4+5+6+7+8= 30+2x

30+2x=36

2x=6

x=3

$1+2+3+4+5+6+7+8 = (1+8)\times \frac{8}{2} = 36$ .

Hence: $36 - 2\times n = 30 \Rightarrow n = 3$ .

The sum of integers from 1 to 8 is 36, but there is a subtracting sign, therefore it takes away twice the value from the 36 because instead of adding we are subtracting, making the required answer as 30. So subtracting sign should be at $\dfrac{6}{2} = \boxed 3$