Utkrisht123

Spoiler for odd

  1   factors 1, 1 sum =2  i.e. 2*1

1 has only 1 as a factor so sum is 1

Spoiler for possibly

Group-one: 83,7,4,5
Group-two: 91,2,6

Good can you find one more

to get marked as best answer because there is one more competitor.

First one to give one more solution will be marked best answer

Spoiler for here's maybe one

Group 1: 18,9,3,6
Group 2: 27, 4,5
both add up to 36

Good can you find one more

to get marked as best answer because there is one more competitor.

1 2 3 4 5 6 7 8 9

Arrange these numbers into two separate groups so that they add up to same total.

Note : you cant turn 9 upside down and make it 6

 

Spoiler for Looks like

You have to turn the 9 into a six.

Numbers 1-9 total 45, which can't be evenly split.
Making the 9 a 6 reduces that total by 3 to 42.
So we need two groups that each total 21.

 

1 2 3 4 5 6 and 6 7 8 should do it.

 

Or turn the 6 into 9, increasing the total by 3 to 48.

 

1 2 3 4 5 9 and 7 8 9 do it for that case.

There is one solution in which you don't have to turn 6 into 9 or 9 into 6

The one who will give me that answer will be marked as best answer

So common guys give it a try

The stipulation that all 31 rectangles are “of the same size” is still a bit ambiguous. The size could be interpreted as area. If rectangles were equal that would imply they are equal in area (2 squares each) and dimensions. However, do we need a stipulation that rectangles must be alined on square boundaries?

If rectangle's dimensions were specified as 1x2, then the problem would be solved by googon97 in post #5.

But those rectangles could be 1/3 x 6, or 1/2 x 4. Still, it is impossible to cover up the board with 31 of those rectangles.

 

Furthermore, can we prove that we could or could not cover the board with 31 equal area (2 squares each) rectangles of any dimensions?  

If you want to then You are welcome to do so