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.
(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
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Posted by Charlie
on 2010-12-07 19:20:15 |
re: piece of cake (solutions?)
