| Clearly No. 9 must have met everyone else: Nos. 1, 2, 3, 4, 5, 6, 7, 8 and (David) Bodycombe. So No. 1 can only have met No. 9. No. 8 doesn't meet No. 1, but as there are only 8 others he must meet all of those. So No. 8 meets Nos. 2, 3, 4, 5, 6, 7, 9 and
Bodycombe. Similarly No. 7 meets Nos. 3, 4, 5, 6, 8, 9 and Bodycombe; No. 6 meets Nos. 4, 5, 7, 8, 9 & Bodycombe; No. 5 meets Nos. 6, 7, 8, 9 &
Bodycombe. At this stage we have described all the meetings since we have described 1 meeting for No. 1, 2 meetings for No. 2, 3 for No. 3, 4 for No. 4 and 5 for No. 5. So all the meetings have been described once and once only. So Bodycombe must have met 5 people: namely Nos, 5, 6, 7, 8 & 9.
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