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                 \ 19-Nov-2025  Bharat Arora   Proof-9             Reader’s Sign _______________________ Date __________








                        •  To get the next bead, add the numbers on the last two beads you used, and use
                           only the ones digit.

                        •  Keep going until you get back to the first and second beads, in that order.

                    Let us make a number bracelet taking the first two number beads as 1 and 3.

                           The first two beads are 1 and 3.                   The third bead is 1 + 3 = 4.

                                          1   3                                        1    3   4

                                Fourth bead = 3 + 4 = 7                      Fifth bead = 4 + 7 = 11; use 1.

                                     1   3    4    7                               1   3    4   7    1

                                 Sixth bead = 7 + 1 = 8                        Seventh bead = 1 + 8 = 9
                                1    3   4    7   1    8                      1    3    4   7    1   8    9

                            Eighth bead = 8 + 9 = 17; use 7.                Ninth bead = 9 + 7 = 16; use 6.

                            1   3    4   7    1   8    9    7          1   3    4   7    1   8    9    7   6

                                                    Tenth bead = 7 + 6 = 13; use 3.

                                              1    3    4   7    1    8    9   7    6    3

                                                       Eleventh bead = 6 + 3 = 9

                                             1   3    4    7   1    8   9    7   6    3   9

                                                   Twelfth bead= 3 + 9 = 12; use 2.

                                           1   3    4   7    1   8    9    7   6    3   9    2

                                                  Thirteenth bead = 9 + 2 = 11; use 1.
                                        1    3   4    7    1   8    9   7    6    3   9    2    1

                                                      Fourteenth bead = 2 + 1 = 3

                                      1   3    4    7   1    8   9    7    6   3    9    2   1    3


                    The last two beads are the same as the first two, so tie                 2     1    3
                    them together with a string to make a bracelet.
                                                                                         9                  4

                                                                                       3                      7


                                                                                         6                   1

                                                                                             7          8
                                                                                                  9





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