Brainteaser 1795: Dicey columns

From The Sunday Times, 9th February 1997 [link]

A boy amused himself by building three separate columns of some equal-sized dice. In each column each die was placed squarely on the one below it. He then looked at the tops of the columns, read each as a digit, and then read the digits together to form one long number.

For example, had the tops been:

then he would have read 113.

He was surprised to find that the number which he read equalled the total number of visible spots all around and on top of his three columns of dice. He also multiplied together the three numbers from the tops of the columns and found that the answer equalled the total number of dice which he had used.

What was that total number of visible spots?

 

For a more challenging Teaser try to find a corresponding situation with more than three columns of dice. There is only one other possibility.

 

The text of this puzzle is taken from the book Brainteasers (2002, edited by Victor Bryant), so may differ from the puzzle originally published in the newspaper.

In fact, the puzzle published in the paper was the more challenging variation.

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