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A piece of pie (Posted on 2010-12-07) Difficulty: 4 of 5
Let N be defined by N=> 3*1*4*1*5*9*2, where each asterisk may be replaced by any basic arithmetic sign ( +, - ,* ,/) and => means that the result is obtained by calculating sequentially from left to right.
Examples: 3+1+4+1+5+9+2=>25; 3+1-4+1-5+9-2=>3; 3*1-4*1-5+9-2=>1 etc.

How many distinct positive integer results can be obtained?
What is the lowest positive integer that cannot be obtained?
What positive integer claims the highest quantity of distinct expressions?
Rem: No brackets allowed.

No Solution Yet Submitted by Ady TZIDON    
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re: piece of cake (solutions?) | Comment 2 of 5 |
(In reply to piece of cake (solutions?) by ed bottemiller)

I get 160 distinct positive integral values, shown with their numbers of occurrence:

1              33 
2              60
3              12
4              29
5              21
6              48
7              34
8              29
9              21
10             30
11             34
12             14
13             26
14             21
15             13
16             20
17             9
18             40
19             14
20             19
21             5
22             22
23             18
24             30
25             15
26             9
27             11
28             23
29             22
30             5
31             2
32             11
33             9
34             12
36             11
37             6
38             14
40             6
41             4
42             20
43             8
44             8
45             5
46             9
47             15
48             2
49             4
50             2
51             6
52             18
53             4
54             23
56             7
58             3
60             2
61             5
62             9
63             2
64             1
65             5
66             2
67             4
68             2
69             2
70             2
71             4
72             14
73             2
74             3
76             2
78             5
81             3
82             1
86             1
87             2
88             10
90             9
91             2
92             6
96             1
97             6
98             6
99             3
101            6
102            4
106            8
108            7
110            8
112            2
115            6
117            1
119            6
124            2
126            5
128            4
132            1
135            5
138            4
142            4
144            2
146            2
148            2
151            4
152            1
155            4
160            2
164            2
168            1
178            3
180            9
182            1
187            2
188            1
191            2
196            1
198            6
200            1
216            8
223            1
227            1
234            6
252            2
268            4
270            4
272            4
288            2
306            4
313            7
317            7
324            2
358            6
360            3
362            6
378            2
396            1
403            2
407            2
450            1
493            2
497            2
538            4
540            4
542            4
583            2
587            2
630            7
673            1
677            1
718            2
720            6
722            2
763            1
767            1
810            2
990            2
1080           4
1170           2
1350           1
1440           2
1530           1

  Posted by Charlie on 2010-12-07 19:20:15
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