Exploding Dots: Overloading Machines!
Number Theory
Level
2
Back to the machine with 4 boxes.
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.
You put in 16 dots (in the right most box). In the final display, what is the number of dots in these boxes?
16
10000
NaN
0001
0000
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
You can start the machine from zero or start it at fifteen. In either case you will end up with a decision to make... you will have two dots in the far left box and you have to ask yourself... will you "create" a new box(in your mind) or will you just let the new dot fade away into nothingness...
Because there are only 4 places to display numbers, I would say the most "correct" answer is 0000. But I encourage you to share the derivations you create. Mathematics begins and ends with each of us.
Every Problem Tells a Story!
( A ⊢ B ) ⟺ ( A ⊨ B )