Dots and Boxes: The 1 ← 2 1\leftarrow2 Machine

Number Theory Level 2

The machine:

  • The dots initially go into the right most box.
  • Whenever there are two (or more) dots are in the same box, then two dots will explode and become one dot on box to the left, unless there is no box one place to the left.

If 14 dots were put into the machine, what is the final number of dots in these boxes?

1011 1110 1001 1010

Peter Michael by Peter Michael , 37, Canada

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2 solutions

Ethan Song
Jul 6, 2017

This machine will just change 14 into its binary form, 1110.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Peter Michael
Jul 6, 2017

With this machine you will see that 7 explosions in the first box, 3 explosions in the next box and 1 explosion in the last box.

If we realize that in 7 is even and 3 is odd and 1 is odd it will tell you where the digits will come from.

You should try to be cognizant of the numeric properties of the solution, in other words what digits are possible in this machine... when all the explosions are finished.

Being aware that in certain in fields you have standard and non-standard forms of situation will need to be considered to consider and derive solutions.

As evidence... did you picture 14 dots going into the machine all at once? Or did you did this set by step?

Neither is incorrect the solution depends on the human thinking about it!

Every Problem Tells a Story!

( A ⊢ B ) ⟺ ( A ⊨ B ) (A\vdash B)\iff(A\vDash B)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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