Maths Help

[PenWise]

Looking for help with this please

I need to find16 different numbers between 1 and 50 so that each number between 1 to 100 can be found.
(a) by adding together no more than two of the original integers;
(b) by merely selecting the required number from the original series; ork
(c) by selecting one of the original integers and doubling it.

Thanks in advance

[fiction-factory]

To start you off, I think 1 has to be in there as that's the only way of making number 1

[jim360]

Seems like this is best answered by trial and error. Write out the numbers from 1 to 100, and, starting from the smallest numbers, pick one and see which numbers are "covered" by choosing that number -- eg if you picked 2 then both 2 and 4 can be found -- and then picking the next smallest number that is missing. And so on. If you don't find a solution then change your choice of (next) smallest number, and so on.

Certainly 1 is needed as there is no other way to cover 1, and also it will become clear quite quickly (I think!) that there can't be a solution using only sixteen numbers that doesn't also use 2. The rest I've not worked through, but I can't see a better approach than this one, building up from the smaller numbers until you have a set that covers every possible number between and including 1 and 100 using the operations given (ie number itself, or double a number, or one number + another).

Good luck. If you still have trouble then I might come back and look at the problem in more detail.

[Fibonacci]

So further thoughts must have 49 & 50 as two of the numbers : as no other way to make 100 (50 x 2) & 99 (50 + 49).
Also even results can be made by doubling or adding two even or two odd numbers but odd results can only be made by adding one odd and one even number.

[PenWise]

Thanks for all the help given, I will start working my way through all the numbers later!!!