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20 Free Bingo

What is the highest number of matching numbers you can get on a Bingo card and not have Bingo?

With Bingo being 5 in a row, column on diagonal, no special Bingo's. I know if the Free Space was a number than it would be 20, but how would you figure it out with the Free Space?

you have 5 by 5 squares

and i assume bingo is 5 across or 5 down or 5 diagonal

that means

in order NOT to have bingo you have to be missing one number from each diagonal and horizontal

and vertical

so you cant have

xxxxx

or
x
x
x
x
x

or
x
..x
.....x
.......x
..........x

so if you miss the diagonal then you will have not win so you are correct with the free space being a number it is 20 everything but the diagonal will give you a loosing ticket

with the free space though that means you will have to pick a number to cancel the middle horizontal and the middle diagonal that is not in the center that would change things

x
..x
.....f.x
.....x....
...........x

i think its the same because as you see from the diagram the numbers we have to choose to keep from bingo would change for the center to the one beside that and the one below or above i chose below ..

you can see that choosing this arrangement will cancel every diagonal and ever horizontal and vertical still and will so so with only 5 numbers missing so again if you count the free as a match its 20 but if you count the free as not a match then its 19 numbers can be drawn without you winning

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