” The essence of mathematics is not to make simple things complicated, but to make complicated things simple” – S. Gudder
2 is an interesting number. First off, it’s the only even prime number. Secondly, all even numbers are divisible by 2. Then there are the powers of 2. That’s when you start with 2 and double it, getting 4. Then double that, getting 8. And again to 16, 32, 64, 128 … it goes on endlessly. These are the powers of 2.
More specifically, 1 has to be added to this set of numbers (it’s the 0th power of 2 or any number for that matter). In any case, the integers that are powers of 2 are the set of numbers {1,2,4,8,16,32,64,128,256,512,…}.
What’s really powerful about this set of numbers is that any positive integer (you read that right – that’s any positive integer) can be made by adding a subset of these numbers. Let’s take a look at an example using the number 23.
- 23 = 16 + 4 + 2 + 1
So there’s 23 as the sum of only powers of 2 (using each no more than once). That’s today’s challenge.
make the numbers 3 through 50 by adding up powers of 2 (using each power only once or not at all)
What’s also interesting is that your answers are unique, there’s only one way to sum the powers of 2 to arrive at each number. To get you started, here are a few
- 3 = 2 + 1
- 4 = 4
- 5 = 4 + 1
Now it’s your turn to figure out the numbers 6 through 50. An interesting pattern will hopefully emerge. Let’s see if you can see it!
Good luck and pass this challenge on to others!
Tags: Number Puzzle, Puzzle