# 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.
@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