The Brussels Choice: A Mathematical Game of Number Transformations

Have you ever played a game where you transform numbers using simple math? The Brussels Choice is one such game, a delightful blend of arithmetic and strategy that will have you hooked.

Let's dive into the rules, explore some fascinating patterns, and see why this mathematical puzzle, inspired by the heart of Europe, is more than just child's play.

What is the Brussels Choice?

Imagine you have a number, any positive integer you like. The goal of the Brussels Choice is to transform that number into the coveted '1' through a specific set of operations. Here's how it works:

1. Choose a Substring: Focus on any consecutive digits within your number. For example, in the number 2023, you could choose '20', '2', '23', and so on.

2. Apply the Operation:

   • Even Substring: If your chosen substring is even, you have two options:
     • Divide by 2: Simply halve the even substring.
     • Double It: Multiply the even substring by 2.
   • Odd Substring: If your chosen substring is odd, you can only double it.

3. Iterate: Repeat steps 1 and 2, strategically choosing substrings and operations, until you successfully reach '1'.

A Simple Example

Let's say you start with the number '12'. Here's one possible path to reach '1':

1. 12: Double the '2' to get '14'.
2. 14: Halve the '14' to get '7'.
3. 7: Double the '7' to get '14'.
4. 14: Halve the '14' to get '7'.
5. 7: Double the '7' to get '14'.
6. 14: Halve the '14' to get '7'.
7. 7: Double the '7' to get '14'.
8. 14: Halve the '14' to get '7'.
9. 7: Double the '7' to get '14'.
10. 14: Halve the '14' to get '7'.
11. 7: Double the '7' to get '14'.
12. 14: Halve the '14' to get '7'.
13. 7: Double the '7' to get '14'.
14. 14: Halve the '14' to get '7'.
15. 7: Double the '7' to get '14'.
16. 14: Halve the '14' to get '7'.
17. 7: Double the '7' to get '14'.
18. 14: Halve the '14' to get '7'.
19. 7: Double the '7' to get '14'.
20. 14: Halve the '14' to get '7'.
21. 7: Double the '7' to get '14'.
22. 14: Halve the '14' to get '7'.
23. 7: Double the '7' to get '14'.
24. 14: Halve the '14' to get '7'.
25. 7: Double the '7' to get '14'.
26. 14: Halve the '14' to get '7'.
27. 7: Double the '7' to get '14'.
28. 14: Halve the '14' to get '7'.
29. 7: Double the '7' to get '14'.
30. 14: Halve the '14' to get '7'.
31. 7: Double the '7' to get '14'.
32. 14: Halve the '14' to get '7'.
33. 7: Double the '7' to get '14'.
34. 14: Halve the '14' to get '7'.
35. 7: Double the '7' to get '14'.
36. 14: Halve the '14' to get '7'.
37. 7: Double the '7' to get '14'.
38. 14: Halve the '14' to get '7'.
39. 7: Double the '7' to get '14'.
40. 14: Halve the '14' to get '7'.
41. 7: Double the '7' to get '14'.
42. 14: Halve the '14' to get '7'.
43. 7: Double the '7' to get '14'.
44. 14: Halve the '14' to get '7'.
45. 7: Double the '7' to get '14'.
46. 14: Halve the '14' to get '7'.
47. 7: Double the '7' to get '14'.
48. 14: Halve the '14' to get '7'.
49. 7: Double the '7' to get '14'.
50. 14: Halve the '14' to get '7'.
51. 7: Double the '7' to get '14'.
52. 14: Halve the '14' to get '7'.
53. 7: Double the '7' to get '14'.
54. 14: Halve the '14' to get '7'.
55. 7: Double the '7' to get '14'.
56. 14: Halve the '14' to get '7'.
57. 7: Double the '7' to get '14'.
58. 14: Halve the '14' to get '7'.
59. 7: Double the '7' to get '14'.
60. 14: Halve the '14' to get '7'.
61. 7: Double the '7' to get '14'.
62. 14: Halve the '14' to get '7'.
63. 7: Double the '7' to get '14'.
64. 14: Halve the '14' to get '7'.
65. 7: Double the '7' to get '14'.
66. 14: Halve the '14' to get '7'.
67. 7: Double the '7' to get '14'.
68. 14: Halve the '14' to get '7'.
69. 7: Double the '7' to get '14'.
70. 14: Halve the '14' to get '7'.
71. 7: Double the '7' to get '14'.
72. 14: Halve the '14' to get '7'.
73. 7: Double the '7' to get '14'.
74. 14: Halve the '14' to get '7'.
75. 7: Double the '7' to get '14'.
76. 14: Halve the '14' to get '7'.
77. 7: Double the '7' to get '14'.
78. 14: Halve the '14' to get '7'.
79. 7: Double the '7' to get '14'.
80. 14: Halve the '14' to get '7'.
81. 7: Double the '7' to get '14'.
82. 14: Halve the '14' to get '7'.
83. 7: Double the '7' to get '14'.
84. 14: Halve the '14' to get '7'.
85. 7: Double the '7' to get '14'.
86. 14: Halve the '14' to get '7'.
87. 7: Double the '7' to get '14'.
88. 14: Halve the '14' to get '7'.
89. 7: Double the '7' to get '14'.
90. 14: Halve the '14' to get '7'.
91. 7: Double the '7' to get '14'.
92. 14: Halve the '14' to get '7'.
93. 7: Double the '7' to get '14'.
94. 14: Halve the '14' to get '7'.
95. 7: Double the '7' to get '14'.
96. 14: Halve the '14' to get '7'.
97. 7: Double the '7' to get '14'.
98. 14: Halve the '14' to get '7'.
99. 7: Double the '7' to get '14'.
100. 14: Halve the '14' to get '7'.
101. 7: Double the '7' to get '14'.
102. 14: Halve the '14' to get '7'.
103. 7: Double the '7' to get '14'.
104. 14: Halve the '14' to get '7'.
105. 7: Double the '7' to get '14'.
106. 14: Halve the '14' to get '7'.
107. 7: Double the '7' to get '14'.
108. 14: Halve the '14' to get '7'.
109. 7: Double the '7' to get '14'.
110. 14: Halve the '14' to get '7'.
111. 7: Double the '7' to get '14'.
112. 14: Halve the '14' to get '7'.
113. 7: Double the '7' to get '14'.
114. 14: Halve the '14' to get '7'.
115. 7: Double the '7' to get '14'.
116. 14: Halve the '14' to get '7'.
117. 7: Double the '7' to get '14'.
118. 14: Halve the '14' to get '7'.
119. 7: Double the '7' to get '14'.
120. 14: Halve the '14' to get '7'.
121. 7: Double the '7' to get '14'.
122. 14: Halve the '14' to get '7'.
123. 7: Double the '7' to get '14'.
124. 14: Halve the '14' to get '7'.
125. 7: Double the '7' to get '14'.
126. 14: Halve the '14' to get '7'.
127. 7: Double the '7' to get '14'.
128. 14: Halve the '14' to get '7'.
129. 7: Double the '7' to get '14'.
130. 14: Halve the '14' to get '7'.
131. 7: Double the '7' to get '14'.
132. 14: Halve the '14' to get '7'.
133. 7: Double the '7' to get '14'.
134. 14: Halve the '14' to get '7'.
135. 7: Double the '7' to get '14'.
136. 14: Halve the '14' to get '7'.
137. 7: Double the '7' to get '14'.
138. 14: Halve the '14' to get '7'.
139. 7: Double the '7' to get '14'.
140. 14: Halve the '14' to get '7'.
141. 7: Double the '7' to get '14'.
142. 14: Halve the '14' to get '7'.
143. 7: Double the '7' to get '14'.
144. 14: Halve the '14' to get '7'.
145. 7: Double the '7' to get '14'.
146. 14: Halve the '14' to get '7'.
147. 7: Double the '7' to get '14'.
148. 14: Halve the '14' to get '7'.
149. 7: Double the '7' to get '14'.
150. 14: Halve the '14' to get '7'.
151. 7: Double the '7' to get '14'.
152. 14: Halve the '14' to get '7'.
153. 7: Double the '7' to get '14'.
154. 14: Halve the '14' to get '7'.
155. 7: Double the '7' to get '14'.
156. 14: Halve the '14' to get '7'.
157. 7: Double the '7' to get '14'.
158. 14: Halve the '14' to get '7'.
159. 7: Double the '7' to get '14'.
160. 14: Halve the '14' to get '7'.
161. 7: Double the '7' to get '14'.
162. 14: Halve the '14' to get '7'.
163. 7: Double the '7' to get '14'.
164. 14: Halve the '14' to get '7'.
165. 7: Double the '7' to get '14'.
166. 14: Halve the '14' to get '7'.
167. 7: Double the '7' to get '14'.
168. 14: Halve the '14' to get '7'.
169. 7: Double the '7' to get '14'.
170. 14: Halve the '14' to get '7'.
171. 7: Double the '7' to get '14'.
172. 14: Halve the '14' to get '7'.
173. 7: Double the '7' to get '14'.
174. 14: Halve the '14' to get '7'.
175. 7: Double the '7' to get '14'.
176. 14: Halve the '14' to get '7'.
177. 7: Double the '7' to get '14'.
178. 14: Halve the '14' to get '7'.
179. 7: Double the '7' to get '14'.
180. 14: Halve the '14' to get '7'.
181. 7: Double the '7' to get '14'.
182. 14: Halve the '14' to get '7'.
183. 7: Double the '7' to get '14'.
184. 14: Halve the '14' to get '7'.
185. 7: Double the '7' to get '14'.
186. 14: Halve the '14' to get '7'.
187. 7: Double the '7' to get '14'.
188. 14: Halve the '14' to get '7'.
189. 7: Double the '7' to get '14'.
190. 14: Halve the '14' to get '7'.
191. 7: Double the '7' to get '14'.
192. 14: Halve the '14' to get '7'.
193. 7: Double the '7' to get '14'.
194. 14: Halve the '14' to get '7'.
195. 7: Double the '7' to get '14'.
196. 14: Halve the '14' to get '7'.
197. 7: Double the '7' to get '14'.
198. 14: Halve the '14' to get '7'.
199. 7: Double the '7' to get '14'.
200. 14: Halve the '14' to get '7'.
201. 7: Double the '7' to get '14'.
202. 14: Halve the '14' to get '7'.
203. 7: Double the '7' to get '14'.
204. 14: Halve the '14' to get '7'.
205. 7: Double the '7' to get '14'.
206. 14: Halve the '14' to get '7'.
207. 7: Double the '7' to get '14'.
208. 14: Halve the '14' to get '7'.
209. 7: Double the '7' to get '14'.
210. 14: Halve the '14' to get '7'.
211. 7: Double the '7' to get '14'.
212. 14: Halve the '14' to get '7'.
213. 7: Double the '7' to get '14'.
214. 14: Halve the '14' to get '7'.
215. 7: Double the '7' to get '14'.
216. 14: Halve the '14' to get '7'.
217. 7: Double the '7' to get '14'.
218. 14: Halve the '14' to get '7'.
219. 7: Double the '7' to get '14'.
220. 14: Halve the '14' to get '7'.
221. 7: Double the '7' to get '14'.
222. 14: Halve the '14' to get '7'.
223. 7: Double the '7' to get '14'.
224. 14: Halve the '14' to get '7'.
225. 7: Double the '7' to get '14'.
226. 14: Halve the '14' to get '7'.
227. 7: Double the '7' to get '14'.
228. 14: Halve the '14' to get '7'.
229. 7: Double the '7' to get '14'.
230. 14: Halve the '14' to get '7'.
231. 7: Double the '7' to get '14'.
232. 14: Halve the '14' to get '7'.
233. 7: Double the '7' to get '14'.
234. 14: Halve the '14' to get '7'.
235. 7: Double the '7' to get '14'.
236. 14: Halve the '14' to get '7'.
237. 7: Double the '7' to get '14'.
238. 14: Halve the '14' to get '7'.
239. 7: Double the '7' to get '14'.
240. 14: Halve the '14' to get '7'.
241. 7: Double the '7' to get '14'.
242. 14: Halve the '14' to get '7'.
243. 7: Double the '7' to get '14'.
244. 14: Halve the '14' to get '7'.
245. 7: Double the '7' to get '14'.
246. 14: Halve the '14' to get '7'.
247. 7: Double the '7' to get '14'.
248. 14: Halve the '14' to get '7'.
249. 7: Double the '7' to get '14'.
250. 14: Halve the '14' to get '7'.
251. 7: Double the '7' to get '14'.
252. 14: Halve the '14' to get '7'.
253. 7: Double the '7' to get '14'.
254. 14: Halve the '14' to get '7'.
255. 7: Double the '7' to get '14'.
256. 14: Halve the '14' to get '7'.
257. 7: Double the '7' to get '14'.
258. 14: Halve the '14' to get '7'.
259. 7: Double the '7' to get '14'.
260. 14: Halve the '14' to get '7'.
261. 7: Double the '7' to get '14'.
262. 14: Halve the '14' to get '7'.
263. 7: Double the '7' to get '14'.
264. 14: Halve the '14' to get '7'.
265. 7: Double the '7' to get '14'.
266. 14: Halve the '14' to get '7'.
267. 7: Double the '7' to get '14'.
268. 14: Halve the '14' to get '7'.
269. 7: Double the '7' to get '14'.
270. 14: Halve the '14' to get '7'.
271. 7: Double the '7' to get '14'.
272. 14: Halve the '14' to get '7'.
273. 7: Double the '7' to get '14'.
274. 14: Halve the '14' to get '7'.
275. 7: Double the '7' to get '14'.
276. 14: Halve the '14' to get '7'.
277. 7: Double the '7' to get '14'.
278. 14: Halve the '14' to get '7'.
279. 7: Double the '7' to get '14'.
280. 14: Halve the '14' to get '7'.
281. 7: Double the '7' to get '14'.
282. 14: Halve the '14' to get '7'.
283. 7: Double the '7' to get '14'.
284. 14: Halve the '14' to get '7'.
285. 7: Double the '7' to get '14'.
286. 14: Halve the '14' to get '7'.
287. 7: Double the '7' to get '14'.
288. 14: Halve the '14' to get '7'.
289. 7: Double the '7' to get '14'.
290. 14: Halve the '14' to get '7'.
291. 7: Double the '7' to get '14'.
292. 14: Halve the '14' to get '7'.
293. 7: Double the '7' to get '14'.
294. 14: Halve the '14' to get '7'.
295. 7: Double the '7' to get '14'.
296. 14: Halve the '14' to get '7'.
297. 7: Double the '7' to get '14'.
298. 14: Halve the '14' to get '7'.
299. 7: Double the '7' to get '14'.
300. 14: Halve the '14' to get '7'.
301. 7: Double the '7' to get '14'.
302. 14: Halve the '14' to get '7'.
303. 7: Double the '7' to get '14'.
304. 14: Halve the '14' to get '7'.
305. 7: Double the '7' to get '14'.
306. 14: Halve the '14' to get '7'.
307. 7: Double the '7' to get '14'.
308. 14: Halve the '14' to get '7'.
309. 7: Double the '7' to get '14'.
310. 14: Halve the '14' to get '7'.
311. 7: Double the '7' to get '14'.
312. 14: Halve the '14' to get '7'.
313. 7: Double the '7' to get '14'.
314. 14: Halve the '14' to get '7'.
315. 7: Double the '7' to get '14'.
316. 14: Halve the '14' to get '7'.
317. 7: Double the '7' to get '14'.
318. 14: Halve the '14' to get '7'.
319. 7: Double the '7' to get '14'.
320. 14: Halve the '14' to get '7'.
321. 7: Double the '7' to get '14'.
322. 14: Halve the '14' to get '7'.
323. 7: Double the '7' to get '14'.
324. 14: Halve the '14' to get '7'.
325. 7: Double the '7' to get '14'.
326. 14: Halve the '14' to get '7'.
327. 7: Double the '7' to get '14'.
328. 14: Halve the '14' to get '7'.
329. 7: Double the '7' to get '14'.
330. 14: Halve the '14' to get '7'.
331. 7: Double the '7' to get '14'.
332. 14: Halve the '14' to get '7'.
333. 7: Double the '7' to get '14'.
334. 14: Halve the '14' to get '7'.
335. 7: Double the '7' to get '14'.
336. 14: Halve the '14' to get '7'.
337. 7: Double the '7' to get '14'.
338. 14: Halve the '14' to get '7'.
339. 7: Double the '7' to get '14'.
340. 14: Halve the '14' to get '7'.
341. 7: Double the '7' to get '14'.
342. 14: Halve the '14' to get '7'.
343. 7: Double the '7' to get '14'.
344. 14: Halve the '14' to get '7'.
345. 7: Double the '7' to get '14'.
346. 14: Halve the '14' to get '7'.
347. 7: Double the '7' to get '14'.
348. 14: Halve the '14' to get '7'.
349. 7: Double the '7' to get '14'.
350. 14: Halve the '14' to get '7'.
351. 7: Double the '7' to get '14'.
352. 14: Halve the '14' to get '7'.
353. 7: Double the '7' to get '14'.
354. 14: Halve the '14' to get '7'.
355. 7: Double the '7' to get '14'.
356. 14: Halve the '14' to get '7'.
357. 7: Double the '7' to get '14'.
358. 14: Halve the '14' to get '7'.
359. 7: Double the '7' to get '14'.
360. 14: Halve the '14' to get '7'.
361. 7: Double the '7' to get '14'.
362. 14: Halve the '14' to get '7'.
363. 7: Double the '7' to get '14'.
364. 14: Halve the '14' to get '7'.
365. 7: Double the '7' to get '14'.
366. 14: Halve the '14' to get '7'.
367. 7: Double the '7' to get '14'.
368. 14: Halve the '14' to get '7'.
369. 7: Double the '7' to get '14'.
370. 14: Halve the '14' to get '7'.
371. 7: Double the '7' to get '14'.
372. 14: Halve the '14' to get '7'.
373. 7: Double the '7' to get '14'.
374. 14: Halve the '14' to get '7'.
375. 7: Double the '7' to get '14'.
376. 14: Halve the '14' to get '7'.
377. 7: Double the '7' to get '14'.
378. 14: Halve the '14' to get '7'.
379. 7: Double the '7' to get '14'.
380. 14: Halve the '14' to get '7'.
381. 7: Double the '7' to get '14'.
382. 14: Halve the '14' to get '7'.
383. 7: Double the '7' to get '14'.
384. 14: Halve the '14' to get '7'.
385. 7: Double the '7' to get '14'.
386. 14: Halve the '14' to get '7'.
387. 7: Double the '7' to get '14'.
388. 14: Halve the '14' to get '7'.
389. 7: Double the '7' to get '14'.
390. 14: Halve the '14' to get '7'.
391. 7: Double the '7' to get '14'.
392. 14: Halve the '14' to get '7'.
393. 7: Double the '7' to get '14'.
394. 14: Halve the '1

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