Math: Five numbers with unique sums
math, numbers, sum, unique
Solution
`1, 10, 100, 10000, 100000` gives you five numbers like you desire.
In general, `1, 10, 100, 1000, ..., 10^k` where `k` is the number of numbers that you need.
And even more general, you can say `b^0, b^1, ..., b^k`, where `b >= 2`. Note that you have the special property that not only are all the pairwise sums unique, but all the subset sums are unique (just look at representations in base `b`).
Problem
So I need a way to figure out how to get 5 numbers, and when you add any 2 of them, it will result in a sum that you can only get by adding those specific two numbers. Here's an example of what I'm talking about, but with 3 numbers: 1 3 5 1 + 3 = 4 1 + 5 = 6 3 + 5 = 8 Adding any two of those numbers will end up with a unique sum that cannot be found by adding any other pair of the numbers. I need to do this, but with 5 different numbers. And if you have a method of figuring out how to do this with any amount of numbers, sharing that would be appreciated as well. Thank you