Â
Construct the 16x16 inlay magic square by combining a grid of  increasing numbers from 1 up to 256 with a grid of decreasing numbers from 256 up to 1.
Â
 16x16 square of increasing numbers from 1 up to 256 |
|||||||||||||||
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 |
70 |
71 |
72 |
73 |
74 |
75 |
76 |
77 |
78 |
79 |
80 |
81 |
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
90 |
91 |
92 |
93 |
94 |
95 |
96 |
97 |
98 |
99 |
100 |
101 |
102 |
103 |
104 |
105 |
106 |
107 |
108 |
109 |
110 |
111 |
112 |
113 |
114 |
115 |
116 |
117 |
118 |
119 |
120 |
121 |
122 |
123 |
124 |
125 |
126 |
127 |
128 |
129 |
130 |
131 |
132 |
133 |
134 |
135 |
136 |
137 |
138 |
139 |
140 |
141 |
142 |
143 |
144 |
145 |
146 |
147 |
148 |
149 |
150 |
151 |
152 |
153 |
154 |
155 |
156 |
157 |
158 |
159 |
160 |
161 |
162 |
163 |
164 |
165 |
166 |
167 |
168 |
169 |
170 |
171 |
172 |
173 |
174 |
175 |
176 |
177 |
178 |
179 |
180 |
181 |
182 |
183 |
184 |
185 |
186 |
187 |
188 |
189 |
190 |
191 |
192 |
193 |
194 |
195 |
196 |
197 |
198 |
199 |
200 |
201 |
202 |
203 |
204 |
205 |
206 |
207 |
208 |
209 |
210 |
211 |
212 |
213 |
214 |
215 |
216 |
217 |
218 |
219 |
220 |
221 |
222 |
223 |
224 |
225 |
226 |
227 |
228 |
229 |
230 |
231 |
232 |
233 |
234 |
235 |
236 |
237 |
238 |
239 |
240 |
241 |
242 |
243 |
244 |
245 |
246 |
247 |
248 |
249 |
250 |
251 |
252 |
253 |
254 |
255 |
256 |
 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
16x16 square of decreasing numbers from 256 up to 1 |
|||||||||||||||
256 |
255 |
254 |
253 |
252 |
251 |
250 |
249 |
248 |
247 |
246 |
245 |
244 |
243 |
242 |
241 |
240 |
239 |
238 |
237 |
236 |
235 |
234 |
233 |
232 |
231 |
230 |
229 |
228 |
227 |
226 |
225 |
224 |
223 |
222 |
221 |
220 |
219 |
218 |
217 |
216 |
215 |
214 |
213 |
212 |
211 |
210 |
209 |
208 |
207 |
206 |
205 |
204 |
203 |
202 |
201 |
200 |
199 |
198 |
197 |
196 |
195 |
194 |
193 |
192 |
191 |
190 |
189 |
188 |
187 |
186 |
185 |
184 |
183 |
182 |
181 |
180 |
179 |
178 |
177 |
176 |
175 |
174 |
173 |
172 |
171 |
170 |
169 |
168 |
167 |
166 |
165 |
164 |
163 |
162 |
161 |
160 |
159 |
158 |
157 |
156 |
155 |
154 |
153 |
152 |
151 |
150 |
149 |
148 |
147 |
146 |
145 |
144 |
143 |
142 |
141 |
140 |
139 |
138 |
137 |
136 |
135 |
134 |
133 |
132 |
131 |
130 |
129 |
128 |
127 |
126 |
125 |
124 |
123 |
122 |
121 |
120 |
119 |
118 |
117 |
116 |
115 |
114 |
113 |
112 |
111 |
110 |
109 |
108 |
107 |
106 |
105 |
104 |
103 |
102 |
101 |
100 |
99 |
98 |
97 |
96 |
95 |
94 |
93 |
92 |
91 |
90 |
89 |
88 |
87 |
86 |
85 |
84 |
83 |
82 |
81 |
80 |
79 |
78 |
77 |
76 |
75 |
74 |
73 |
72 |
71 |
70 |
69 |
68 |
67 |
66 |
65 |
64 |
63 |
62 |
61 |
60 |
59 |
58 |
57 |
56 |
55 |
54 |
53 |
52 |
51 |
50 |
49 |
48 |
47 |
46 |
45 |
44 |
43 |
42 |
41 |
40 |
39 |
38 |
37 |
36 |
35 |
34 |
33 |
32 |
31 |
30 |
29 |
28 |
27 |
26 |
25 |
24 |
23 |
22 |
21 |
20 |
19 |
18 |
17 |
16 |
15 |
14 |
13 |
12 |
11 |
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
= magic 16x16 square (combination of the two grids) |
|||||||||||||||
1 |
255 |
254 |
4 |
5 |
251 |
250 |
8 |
9 |
247 |
246 |
12 |
13 |
243 |
242 |
16 |
240 |
18 |
19 |
237 |
236 |
22 |
23 |
233 |
232 |
26 |
27 |
229 |
228 |
30 |
31 |
225 |
224 |
34 |
35 |
221 |
220 |
38 |
39 |
217 |
216 |
42 |
43 |
213 |
212 |
46 |
47 |
209 |
49 |
207 |
206 |
52 |
53 |
203 |
202 |
56 |
57 |
199 |
198 |
60 |
61 |
195 |
194 |
64 |
65 |
191 |
190 |
68 |
69 |
187 |
186 |
72 |
73 |
183 |
182 |
76 |
77 |
179 |
178 |
80 |
176 |
82 |
83 |
173 |
172 |
86 |
87 |
169 |
168 |
90 |
91 |
165 |
164 |
94 |
95 |
161 |
160 |
98 |
99 |
157 |
156 |
102 |
103 |
153 |
152 |
106 |
107 |
149 |
148 |
110 |
111 |
145 |
113 |
143 |
142 |
116 |
117 |
139 |
138 |
120 |
121 |
135 |
134 |
124 |
125 |
131 |
130 |
128 |
129 |
127 |
126 |
132 |
133 |
123 |
122 |
136 |
137 |
119 |
118 |
140 |
141 |
115 |
114 |
144 |
112 |
146 |
147 |
109 |
108 |
150 |
151 |
105 |
104 |
154 |
155 |
101 |
100 |
158 |
159 |
97 |
96 |
162 |
163 |
93 |
92 |
166 |
167 |
89 |
88 |
170 |
171 |
85 |
84 |
174 |
175 |
81 |
177 |
79 |
78 |
180 |
181 |
75 |
74 |
184 |
185 |
71 |
70 |
188 |
189 |
67 |
66 |
192 |
193 |
63 |
62 |
196 |
197 |
59 |
58 |
200 |
201 |
55 |
54 |
204 |
205 |
51 |
50 |
208 |
48 |
210 |
211 |
45 |
44 |
214 |
215 |
41 |
40 |
218 |
219 |
37 |
36 |
222 |
223 |
33 |
32 |
226 |
227 |
29 |
28 |
230 |
231 |
25 |
24 |
234 |
235 |
21 |
20 |
238 |
239 |
17 |
241 |
15 |
14 |
244 |
245 |
11 |
10 |
248 |
249 |
7 |
6 |
252 |
253 |
3 |
2 |
256 |
Â
Â
Construct on website http://users.eastlink.ca/~sharrywhite/BorderedMagicSquares.html a concentric 18x18 magic square and use only the border. Because the border consists of the numbers 1 up to 34 (and 291 up to 324) we add 34 to all numbers of the 16x16 inlay magic square.
Â
Â
 16x16 in 18x18 magic square
307 |
25 |
301 |
23 |
303 |
21 |
305 |
19 |
316 |
1 |
309 |
15 |
311 |
13 |
313 |
11 |
315 |
17 |
298 |
35 |
289 |
288 |
38 |
39 |
285 |
284 |
42 |
43 |
281 |
280 |
46 |
47 |
277 |
276 |
50 |
27 |
28 |
274 |
52 |
53 |
271 |
270 |
56 |
57 |
267 |
266 |
60 |
61 |
263 |
262 |
64 |
65 |
259 |
297 |
296 |
258 |
68 |
69 |
255 |
254 |
72 |
73 |
251 |
250 |
76 |
77 |
247 |
246 |
80 |
81 |
243 |
29 |
30 |
83 |
241 |
240 |
86 |
87 |
237 |
236 |
90 |
91 |
233 |
232 |
94 |
95 |
229 |
228 |
98 |
295 |
294 |
99 |
225 |
224 |
102 |
103 |
221 |
220 |
106 |
107 |
217 |
216 |
110 |
111 |
213 |
212 |
114 |
31 |
32 |
210 |
116 |
117 |
207 |
206 |
120 |
121 |
203 |
202 |
124 |
125 |
199 |
198 |
128 |
129 |
195 |
293 |
292 |
194 |
132 |
133 |
191 |
190 |
136 |
137 |
187 |
186 |
140 |
141 |
183 |
182 |
144 |
145 |
179 |
33 |
34 |
147 |
177 |
176 |
150 |
151 |
173 |
172 |
154 |
155 |
169 |
168 |
158 |
159 |
165 |
164 |
162 |
291 |
26 |
163 |
161 |
160 |
166 |
167 |
157 |
156 |
170 |
171 |
153 |
152 |
174 |
175 |
149 |
148 |
178 |
299 |
8 |
146 |
180 |
181 |
143 |
142 |
184 |
185 |
139 |
138 |
188 |
189 |
135 |
134 |
192 |
193 |
131 |
317 |
318 |
130 |
196 |
197 |
127 |
126 |
200 |
201 |
123 |
122 |
204 |
205 |
119 |
118 |
208 |
209 |
115 |
7 |
6 |
211 |
113 |
112 |
214 |
215 |
109 |
108 |
218 |
219 |
105 |
104 |
222 |
223 |
101 |
100 |
226 |
319 |
320 |
227 |
97 |
96 |
230 |
231 |
93 |
92 |
234 |
235 |
89 |
88 |
238 |
239 |
85 |
84 |
242 |
5 |
4 |
82 |
244 |
245 |
79 |
78 |
248 |
249 |
75 |
74 |
252 |
253 |
71 |
70 |
256 |
257 |
67 |
321 |
322 |
66 |
260 |
261 |
63 |
62 |
264 |
265 |
59 |
58 |
268 |
269 |
55 |
54 |
272 |
273 |
51 |
3 |
2 |
275 |
49 |
48 |
278 |
279 |
45 |
44 |
282 |
283 |
41 |
40 |
286 |
287 |
37 |
36 |
290 |
323 |
308 |
300 |
24 |
302 |
|