# Equally distributing cards on a table. (interpolation)

this problem is originally from a programming task i am on.

there is a number of playing cards n. the width of each card is w.

now the cards should be placed next to each other on a table with equal space. the table's width is also limited, let's call this t. so t is the available width that should be used by the cards.

now i am looking for a spacing-distance that should be put between each card depending on the above variables. cards can overlap.

so far i simply tried to interpolate depending on the number of cards, but it doesnt work out very well. i think i am missing to take the card width into account, but i dont know how.

thanks!

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Let the distance between the centers of adjacent cards be $x$. Then $(n-1)x+w=t$, so $x=(t-w)/(n-1)$. That tells you how far apart to put (the centers of) adjacent cards.

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thanks, but in general the width of a card is a lot smaller than the width of the table. so your formula will give negative values. is that on purpose? – clamp Jul 12 '11 at 12:44
@clamp: Given your variables, $t \gt w,$ so $x \gt 0$. I don't see a negative answer. Say the table is $30$ inches, and $18$ cards are $1$ inch each. Then $x=\frac{29}{17}$ – Ross Millikan Jul 12 '11 at 12:50
well the formula was w-t before the edit. – clamp Jul 12 '11 at 13:29
Thanks, Chris, for fixing my typo. clamp, people make mistakes; what you do when you run into one is go back one equation and see if you can figure out what went wrong. My first equation was right, and even though I failed to solve it correctly, perhaps you could have? – Gerry Myerson Jul 13 '11 at 1:42