Counting on a Clock
On a standard clock face, put your finger on 1. Move clockwise 1 space
to land on 2. Move 2 spaces to land on 4. Move 4 spaces to land on
8. Move 8 spaces to again land on 4. Thus, the standard clock face
doesn't let us reach every number in this way.
- Is it possible to arrange the 12 numbers on the clock face so that you
can start on 1 and end on 12 and reach every number in between? Each
move is the clockwise number of spaces corresponding to the number being
pointed to. If not, can you start with a different number?
- Arrange the numbers on a clock face similarly to the previous problem.
In this case, each move is equal to the number of letters in the name of
each number (one, two, three, four, five, six, seven, eight, nine, ten,
eleven, twelve.) Extension: Can you start on 1 and end on 1 after
visiting all other numbers?
- Replace the numbers with a single suit of cards from a standard deck
(Ace=1, Jack=11, Queen=12). Using the spelling of each card, can you
create an arrangement on the clock face to run from Ace to Queen hitting all
cards in between? From Ace to Ace?
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