+----+----+----+----+
| 23 | | | |
+----+----+----+----+
| | | 64 | |
+----+----+----+----+
| | N | | |
+----+----+----+----+
| | | |101 |
+----+----+----+----+
In the 4x4 grid provided above:
- Each the 16 values appearing in the 16 cells is a positive integer.
- The 4 values corresponding to each of the 4 rows are in arithmetic sequence.
- The 4 values corresponding to each of the 4 columns are in arithmetic sequence.
Determine the total number of
distinct positive integer values that N can assume.
Adding this code:
for col=1:4
increm=(grid(4,col)-grid(1,col))/3;
grid(2,col)=grid(1,col)+increm;
grid(3,col)=grid(1,col)+2*increm;
end
allows the full grid values to show:
grid =
23 16 9 2
122 93 64 35
221 170 119 68
320 247 174 101
grid =
23 17 11 5
118 91 64 37
213 165 117 69
308 239 170 101
grid =
23 18 13 8
114 89 64 39
205 160 115 70
296 231 166 101
grid =
23 19 15 11
110 87 64 41
197 155 113 71
284 223 162 101
grid =
23 20 17 14
106 85 64 43
189 150 111 72
272 215 158 101
grid =
23 21 19 17
102 83 64 45
181 145 109 73
260 207 154 101
grid =
23 22 21 20
98 81 64 47
173 140 107 74
248 199 150 101
grid =
23 23 23 23
94 79 64 49
165 135 105 75
236 191 146 101
grid =
23 24 25 26
90 77 64 51
157 130 103 76
224 183 142 101
grid =
23 25 27 29
86 75 64 53
149 125 101 77
212 175 138 101
grid =
23 26 29 32
82 73 64 55
141 120 99 78
200 167 134 101
grid =
23 27 31 35
78 71 64 57
133 115 97 79
188 159 130 101
grid =
23 28 33 38
74 69 64 59
125 110 95 80
176 151 126 101
grid =
23 29 35 41
70 67 64 61
117 105 93 81
164 143 122 101
grid =
23 30 37 44
66 65 64 63
109 100 91 82
152 135 118 101
grid =
23 31 39 47
62 63 64 65
101 95 89 83
140 127 114 101
grid =
23 32 41 50
58 61 64 67
93 90 87 84
128 119 110 101
grid =
23 33 43 53
54 59 64 69
85 85 85 85
116 111 106 101
grid =
23 34 45 56
50 57 64 71
77 80 83 86
104 103 102 101
grid =
23 35 47 59
46 55 64 73
69 75 81 87
92 95 98 101
grid =
23 36 49 62
42 53 64 75
61 70 79 88
80 87 94 101
grid =
23 37 51 65
38 51 64 77
53 65 77 89
68 79 90 101
grid =
23 38 53 68
34 49 64 79
45 60 75 90
56 71 86 101
grid =
23 39 55 71
30 47 64 81
37 55 73 91
44 63 82 101
grid =
23 40 57 74
26 45 64 83
29 50 71 92
32 55 78 101
grid =
23 41 59 77
22 43 64 85
21 45 69 93
20 47 74 101
grid =
23 42 61 80
18 41 64 87
13 40 67 94
8 39 70 101
|
|
Posted by Charlie
on 2023-02-13 19:17:32 |
the full grids
