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                 \ 18-Nov-2025  Bharat Arora   Proof-9             Reader’s Sign _______________________ Date __________








                                                  Fun                  Activity                 21 st

                                                                                              Century   #Critical Thinking
                                                                                               Skills
                                                          King’s Horses


                    A king has 32 horses. He has arranged them in a square, as shown in the figure given
                    below,  such that he can see 12 horses along each line of sight, as indicated in the

                    picture.











































                    The king has instructed the watchman to make sure there are 32 horses all the time,

                    no more, no less. Every circle must have at least one horse. The watchman thinks he is
                    smart and so has devised a shortcut to verify this. Regardless of the number of horses

                    in each circle, he just checks the total number of horses along each line of sight.

                    One evening a traveller comes and meets the watchman. He has four
                    identical horses and wants to tie them along with these 32 horses. The

                    watchman refuses initially but agrees later when an incentive is offered.
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                                                                                            Large Numbers
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