Luis's Random Calculation

Let $x$ be the minimum and $y$ be the maximum answer Luis could get.

$x = 0 + 0 - 9 = -9$

$y = 9 + 9 - 0 = 18$

Then the answer of Luis could get is in the range $-9, -8, \ldots, 18$ imply $18 + 9 + 1 = 28$ different answers.

To solve this problem, all we need to do is find a minimum value that he could get and a maximum value that he can get and count how many numbers are in between them. The minimum value he can get is 0 + 0 - 9 = -9 and the maximum value he can get is 9 + 9 - 0 = 18. Thus the total number of answers that Luis can get are 18 + 9 + 1 (for zero) = 28 answers

All of the answers given lack something in common.All of them finally reach the answer 28 but none of which proves the fact that all 28 integers in the interval [-9,18] can be achieved.I don't really know how to prove that except for writing an example for all 28 cases but I assume there must be another proof in this case.

Largest possible solution would be 9 + 9 - 0 = 18 and the smallest possible solution is 0 + 0 - 9 = -9 18 - (-9) = 27 and then add 1 to count the possibility of getting zero and you have 28 possible solutions

The largest possible answer is $18$ since $9+9-0$ is $18$ . The smallest possible answer is $-9$ since $0+0-9$ is $-9$ . There are $28$ integers greater than or equal to $-9$ and less than or equal $18$ .

let the operation be a+b-c, by associating (b-c) you get an answer between -9 and 9 (-9, -8, ..., -1, 0, 1, ..., 9) then you can only add a positive number from 0 to 9, so the greatest number you get is 18, the total of this is 28 numbers: -9,-8, ..., 18

The greatest answer Luis could get is $9 + 9 - 0 = 18$ , and the lowest is $0+0-9$ Then there are $18 + 9 + 1 = 28$ different answers (the 1 is because we must add zero)

The smallest answer is -9 (0+0-9). The greatest is 18 (9+9-0).

18-(-9)+1=28

• it's obvious that all the different answer's Luis could get are integers ,, so we can get the largest value and the lowest value the answer could be , and assuming that ' A ' is the first digit , ' B ' is the second and ' C ' is the third , w can get all the integers ( odd and even ) numbers between the largest and the lowest value by this calculation A + B - C .
• * in details * we can get the largest number when ' A ' and ' B ' are the largest digit , and that's 9 , and when ' C ' is the lowest integer 0 SO A + B - C = 9 + 9 - 0 = 18 is the largest value and it means that A + B - C = 0 + 0 - 9 = -9 is the lowest value
• now it's obvious that the number of the different answers are all the 18's positive numbers and the 9's negative numbers and the Zero 0 :- 18 + 9 +1 = 28

$max=9+9-0=18$ and $min=0+0-9=-9$ so all possible answer is [possitive count]+[zero count]+[negarive count]= $18+1+9=28$

O maior resultado possível é 9+9-0=18

E o menor é 0+0-9=-9

18-(-9)=27

Como há a possibilidade do zero sair também, temos 27+1=28 diferentes respostas.

The minimum answer you can get is -9 (i.e,0+0-9),and the maximum answer you can get is 18 (i.e,9+9-0) . Also that all the answers between these two numbers is possible to get. therefore the total number of answers = 28 [i.e.,18-(-9)+1,(including the end points)]

We must first get the highest possible value which is 9 + 9 - 0 = 18 and get the lowest possible value which is 0 + 0 - 9 = -9

the absolute value of these two numbers are 18 and 9 but remember, 0 is a part of the solution set but is not recognized in these two absolute values. thus,

18 + 9 + n{0} = 18 + 9 + 1 = 28