Question 1203135
.


This problem is posed incorrectly and is  SELF-CONTRADICTING.


If to understand it precisely as it is written,  then the set of all possible solutions is in this table below


<pre>
 n    First    Second    The         The          The 
      number   number    sum      difference     pairs
 ---------------------------------------------------------
 1      23       22       45          1          (23,22)
 2      24       21       45          3          (24,21)
 3      25       20       45          5          (25,20)
 4      26       19       45          7          (26,19)
 5      27       18       45          9          (27,18)

 6      22       23       45         -1          (22,23)
 7      21       24       45         -3          (21,24)
 8      20       25       45         -5          (20,25)
 9      19       26       45         -7          (19,26)
10      18       27       45         -9          (18,27)

11      17       28       45        -11          (17,28)
12      16       29       45        -13          (16,29)
13      15       30       45        -15          (15,30)
14      14       31       45        -17          (14,31)
15      13       32       45        -19          (13,32)

16      12       33       45        -21          (12,33)
17      11       34       45        -23          (11,34)
18      10       35       45        -25          (10,35)
19       9       36       45        -27          ( 9,36)
20       8       37       45        -29          ( 8,37)

21       7       38       45        -31          ( 7,38)
22       6       39       45        -33          ( 6,39)
23       5       40       45        -35          ( 5,40)
24       4       41       45        -37          ( 4,41)
25       3       42       45        -39          ( 3,42)

26       2       43       45        -41          ( 2,43)
27       1       44       45        -43          ( 1,44)
</pre>


As you see, &nbsp;there are &nbsp;27 &nbsp;solutions, &nbsp;which number &nbsp;27 &nbsp;is not in your list of possible answers.


All &nbsp;27 &nbsp;pairs in the last column are different and satisfy the problem's requirement.


Therefore, &nbsp;the conclusion is: &nbsp;the problem formulation is &nbsp;FATALLY &nbsp;and &nbsp;TOTALLY &nbsp;wrong.


I clearly understand that this problem, &nbsp;as presented in this post, &nbsp;migrates in the &nbsp;Internet 
from site to site during the years, &nbsp;while its right place is in &nbsp;GARBAGE &nbsp;BIN.


I saw this problem &nbsp;(or similar, &nbsp;or in similar formulations) at this forum &nbsp;years ago, 
and saw discussions of it by different tutors.


My point of view is that such &nbsp;GIBBERISH &nbsp;does not deserve any discussion.
What it really deserves, &nbsp;is to be removed/deleted from the &nbsp;Internet.