6/09/2015
Imagine that it is the year 4,444 and the world is starting to run out of numbers. We have been recycling soda cans for years, but we never thought we needed to recycle numbers - we calculate things all the time, but we just throw the numbers away when we are done with them.
Fortunately we have figured out how to make artificial 4s, so we have plenty of 4s for now.
The government has a special assignment for you. They want you to invent a new numbering system so that we can write any number we want using only the number 4, along with any mathematical symbol you need. In fact, our supply of 4s is so good that for each number you want to express you can use up to four 4s. Infact the President says he would like you to use four 4s for each number in you new system.
For (no pun intended) example since we are out of "zeros", if you wanted to write a "zero" you could instead write 44 - 44. Or if you wanted to write the number "one" you could write 44/44.
So, how far do you think you can go - using only four 4s and any mathematical symbols you want (but you can't spell a number).
0 =
1 =
2 =
3 =
4 =
5 =
6 =
7 =
8 =
9 =
10 =
11 =
12 =
13 =
14 =
15 =
16 =
17 =
18 =
19 =
20 =
21 =
22 =
23 =
24 =
25 =
26 =
27 =
28 =
29 =
30 =
31 =
32 =
33 =
34 =
35 =
36 =
37 =
38 =
39 =
40 =
Don't stop here - the world needs your help - keep going as far as you can.
David
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