Madeleine types her three-digit Personal Identification Number (PIN) into this keypad. All three digits are different, but the buttons for the first and second digits share an edge, and the buttons for the second and third digits share an edge. For instance, 563 is a possible PIN, but 536 is not, since 5 and 3 do not share an edge. How many possibilities are there for Madeleine’s PIN?
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Australian Mathematics Competition 2020 - Junior (2020)
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