At the Arithmetic Company, to try and cut down labor costs the administration commissioned a calculator to be made. The calculator was produced, and in the quality control division was tested with the following values:
20 + 3 = 23
5 + 15 = 20
7 + 9 + 9 = 25
28 - 22 + 2 = 8
33 - 20 + 4 = 17
71 + 5 - 75 = 1
30 + 19 - 5 = 44
45 + 36 - 23 = 58
Finding all the results satisfactory they put the calculator to use. The first client requested various sums of 2, and using the calculator, was given the following list:
2 + 2 = 85
2 + 2 + 2 = 150
2 + 2 + 2 + 2 = 152
2 + 2 + 2 + 2 + 2 = 232
2 + 2 + 2 + 2 + 2 + 2 = 1114
2 + 2 + 2 + 2 + 2 + 2 + 2 = 1167
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 2227
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 17727
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 24727
The next client requests some consecutive sequences and was given:
1 + 2 + 3 + 4 = 130
5 + 6 + 7 + 8 = 130
9 + 10 + 11 + 12 = 188
13 + 14 + 15 + 16 = 1216
17 + 18 + 19 + 20 = 1157
Finally the last client requests just one sum and is given:
1 + 1 = ERROR
The next day they received many complaints from their clients, and decide to bring in you, their best analyst, to figure out what the calculator is doing. Your job is to find the rules that the determine the calculator's output as well as one example sum (not listed above) so that your method can be tested.
Bonus: What does the calculator output when given 1×1 ?
People may ask any number of additional sums to the calculator in the chat room http://chat.stackexchange.com/rooms/22378/sum-requests:
0 + 0 = ERROR
1 + 2 = ERROR
1 - 3 = ERROR
2 - 7 = ERROR
3 + 3 = ERROR
4 + 4 = ERROR
5 + 19 = ERROR
19 + 5 = ERROR
76 - 75 = ERROR
130 - 85 = ERROR
1 - 2 + 3 + 4 = ERROR
2 + 2 - 2 = 2
15 = 7
15 + 5 = 20
18 = 18
19 = 19
7 + 40 = 25
29 = 25
13 + 4 = 26
39 = 35
5 + 5 = 40
9 + 9 = 40
40 = 40
49 - 5 = 40
5 + 5 + 5 = 45
49 = 45
59 = 55
6 + 2 = 70
5 + 5 + 5 + 5 = 72
85 = 85
3 + 7 = 91
2 + 85 = 150
85 + 2 = 150
85 + 85 = 152
71 + 5 = 303
45 + 13 = 517
If necessary, I'll provide a new hint for few days the problem remains unsolved.
Hint 1: When inputting solitary numbers into the calculator you get the following results:
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 5
10 = 10
Hint 2:
55 + 1 = 35
59 + 1 = 35
65 + 1 = 107
69 + 1 = 107
75 + 1 = 303
79 + 1 = 303
Hint 3:
15 + 3 = 91
19 + 3 = 35