We start with three variables: the total number of rows in the
triangle; the number of pebbles in a row; and the total number of
pebbles, which is what we want to calculate. These variables can be
named `number-of-rows`

, `number-of-pebbles-in-row`

, and
`total`

, respectively.

Both `total`

and `number-of-pebbles-in-row`

are used only
inside the function and are declared with `let`

. The initial
value of `total`

should, of course, be zero. However, the
initial value of `number-of-pebbles-in-row`

should be equal to
the number of rows in the triangle, since the addition will start with
the longest row.

This means that the beginning of the `let`

expression will look
like this:

(let ((total 0) (number-of-pebbles-in-row number-of-rows))body...)

The total number of pebbles can be found by repeatedly adding the number of pebbles in a row to the total already found, that is, by repeatedly evaluating the following expression:

(setq total (+ total number-of-pebbles-in-row))

After the `number-of-pebbles-in-row`

is added to the `total`

,
the `number-of-pebbles-in-row`

should be decremented by one, since
the next time the loop repeats, the preceding row will be
added to the total.

The number of pebbles in a preceding row is one less than the number of
pebbles in a row, so the built-in Emacs Lisp function `1-`

can be
used to compute the number of pebbles in the preceding row. This can be
done with the following expression:

(setq number-of-pebbles-in-row (1- number-of-pebbles-in-row))

Finally, we know that the `while`

loop should stop making repeated
additions when there are no pebbles in a row. So the test for
the `while`

loop is simply:

(while (> number-of-pebbles-in-row 0)

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