[UPDATE Oct. 9: Photos have surfaced on MacRumors suggesting that Walmart could begin selling iPads next week and could have them in 1,000 stores before the end of October.]

[UPDATE Oct. 4: As of Monday, the iPad is also available on Amazon. Click here for pricing.]

One way to track how rapidly Apple (AAPL) is building iPads is to watch where they are being sold.

When it first arrived in April, the device was available only at a couple hundred U.S.-based Apple Stores and, in very short supply, at some BestBuy (BBY) outlets. In less than two days, the shelves were empty.

It wasn’t until late August that supplies caught up to demand. By then Apple was selling the iPad in 19 countries and was set to expand sales to five South American countries and China, where it would be sold at Apple’s four stores on the mainland and selected China Unicom (CHU) outlets.

Then on Sunday the iPad arrived at Target’s (TGT) 1,743 U.S. outlets, roughly doubling its retail presence overnight.

On Sept. 23, Piper Jaffray’s Gene Munster predicted that total iPad points of purchase would exceed the Mac’s by 2011. Ten days, it had happened. By our count:

• 25 countries
• 221 U.S. Apple Stores plus a few dozen overseas outlets
• 1,093 BestBuy stores
• 1,743 Target stores

But there are still 82 shopping days until Christmas, plenty of time to expand some more.

In May, Bloomberg Businessweek reported that Walmart (WMT) was expecting to offer the iPad for sale at “some U.S. stores” before the end of 2010, a move that could re-double the iPads’ retail presence. The numbers, according to the company’s website:

• 2,815 Walmart Supercenters in the U.S.
• 774 Walmart Discount stores

The question once again is whether Apple can build the things fast enough to meet demand.

See also:

• At last: Next-day shipping for the iPad
• Apple has run out of iPads
• iPad international launch postponed
• iPad demand outstrips supply, again
• iPad supply catching up to demand

[Follow Philip Elmer-DeWitt on Twitter @philiped]