
666 F.Supp. 661 (1987)
MOLECULON RESEARCH CORPORATION, Plaintiff,
v.
CBS, INC., Defendant.
Civ. A. No. 82-289-WKS.
United States District Court, D. Delaware.
July 6, 1987.
*662 Thomas S. Lodge, Connolly, Bove, Lodge & Hutz, Wilmington, Del., Robert X. Perry, Jr., J. Carter McKaig, Marc C. Dorigan, Emilio Daddario, Wilkes, Artis, Hedrick & Lane, Washington, D.C., W. Brown Morton, Jr., Warsaw, Va., for plaintiff.
Walter L. Pepperman, II, Morris, Nichols, Arsht & Tunnell, Wilmington, Del., Lewis H. Eslinger, William E. Pelton, Abigail F. Cousins, Eslinger & Pelton, New York City, for defendant.

OPINION
STAPLETON, Circuit Judge:[*]
Claims 3 through 5 of U.S. Patent No. 3,655,201 (the '201 patent) read as follows:
3. A method for restoring a preselected pattern from sets of pieces which pieces have constantly exposed and constantly nonexposed surfaces, the exposed surfaces adapted to be combined to form the preselected pattern, which sets when in random engagement fail to display said preselected pattern which comprises:
a. engaging eight cube pieces as a composite cube;
b. rotating a first set of cube pieces comprising four cubes about a first axis;
c. rotating a second set of four cubes about a second axis; and
d. repeating steps (b) and (c) until the preselected pattern is achieved.
4. The method of claim 3 which includes rotating sets of cubes about one of three mutually perpendicular axes with reference to the composite structure.
5. The method of claim 3 wherein the sets of cubes are rotated through multiples of 90°.
After trial on the issues of validity and infringement, this court held these claims valid and literally infringed by the wellknown Rubik's Cube puzzle and its less familiar cousins, the Rubik's Pocket Cube puzzle and the Rubik's Revenge puzzle. 594 F.Supp. 1420 (D.Del.1984). On appeal, the United States Court of Appeals for the Federal Circuit affirmed this court's validity determinations and its finding that Rubik's Pocket Cube literally infringed the patent. The Court of Appeals vacated this court's finding of literal infringement by Rubik's Cube and Rubik's Revenge, however, and remanded the case so that this court could determine "whether solving the 3x3x3 Rubik's Cube or the 4x4x4 Rubik's Revenge would infringe claims 3-5 under the doctrine of equivalents." 793 F.2d *663 1261, 1272 (Fed.Cir.1986). In the words of the Court of Appeals,
The question there is whether the methods for restoring the Rubik's puzzles with their structural differences and the claimed invention perform substantially the same function in substantially the same way to give substantially the same result.
793 F.2d at 1272.
The opinion of the Court of Appeals establishes at least three things that are of importance in the present context:
1. Claims 3 through 5 "are directed to `a method for restoring a preselected pattern.' They claim a general approach for solving the puzzle." 793 F.2d at 1269.
2. The phrase "engaging ... pieces as a composite cube" refers broadly to holding the pieces together in the shape of a composite cube while permitting the described rotation. It does not limit the claims to the means of engagement suggested in the specifications of the patent. This is clear from the fact that the Court of Appeals affirmed the finding of this court that the 2x2x2 Rubik's Pocket Cube literally infringed claims 3 through 5. 793 F.2d at 1272. While Rubik's Pocket Cube, like Rubik's Cube and Rubik's Revenge, employs mechanical means of engagement, it does not employ magnates, a tongue-in-groove mechanism, or a pop-in snap mechanism as suggested in the specifications of the '201 patent.
3. The concept of "cube pieces" in the phrase "engaging eight cube pieces" is "not limited to geometrically true cubes but refers to the cubelet shape as perceived by the puzzle user." 793 F.2d at 1272. The predicate for this conclusion is that the claims of the '201 patent describe the invention as it appears to a puzzle user.
The parties agree that with two significant exceptions[1] all elements of claims 3 through 5, as interpreted by the Court of Appeals, literally read on Rubik's Cube and Rubik's Revenge. The two exceptions are the phrase "engaging eight cube pieces in a composite cube," and the references to rotating sets of four cubes. Moleculon concedes, as it must for present purposes, that this phrase and these references do not literally read on Rubik's Cube and Rubik's Revenge. It asserts, however, that puzzles, like Rubik's Cube and Rubik's Revenge, which appear to the puzzle user to be a composite cube having 27 or 54 constituent cube pieces and rotateable sets of 9 or 16 cube pieces, respectively, perform substantially the same function as the claimed invention in substantially the same way to give substantially the same result. CBS denies that this is the case. Given the guidance afforded by the opinion of the Court of Appeals, I am constrained to agree with Moleculon.
When one focuses on the fact that claims 3 through 5 claim a general method of playing with a puzzle by randomizing and then restoring a preexisting pattern, it becomes apparent that a composite cube puzzle appearing to have 27 constituent cube pieces and sets of nine cube pieces each rotatable around three mutually perpendicular axes is the functional equivalent of a composite cube puzzle appearing to have eight constituent cube pieces and sets of four cube pieces each rotatable around three mutually perpendicular axes. Both configurations function to entertain the puzzle user by presenting the same type of puzzle problem. Both perform this function in substantially the same way, that is by the rotation of sets of cubes about three mutually perpendicular axes to first randomize and then restore the preexisting *664 pattern. And the result in each instance is a restored pattern on six surfaces. The same can be said for a similar puzzle appearing to have 54 constituent cube pieces and sets of 16 cube pieces rotatable around three mutually perpendicular axes. While it is true that additional complexity is introduced when one progresses from a 2x2x2 composite cube to a 3x3x3 composite cube and then to a 4x4x4 composite cube, this does not substantially alter the function of the puzzle. Each has a similar challenge and the degree of challenge is a matter of personal preference.[2]
This view is confirmed by virtually all the expert testimony in the record. Messrs. Slocum, Zimmerman and Nichols, for example, each referred to the Rubik's Cube as simply another embodiment of the concept disclosed in the '201 patent. Similarly, Erno Rubik himself refers to the equivalence of a 2x2x2 puzzle and a 3x3x3 puzzle in his patent on Rubik's Cube. Indeed, counsel for CBS candidly conceded at oral argument that any puzzle designer would find it obvious to substitute a composite cube appearing to have 27 or 54 constituent cube pieces for a composite cube appearing to have 8 constituent cube pieces:
The next question is ... whether or not the added complexity and challenge would be obvious to one in the art. We don't contest that. Obviously, anyone looking at a two-by-two would consider it to be obvious to go to a three-by-three or four-by-four, and to know that it is more complex.
There is no dispute about that at all. The important question on that is whether or not the puzzle that results from that would have been obvious.
In other words, simply thinking of expanding a two-by-two-by-two to a three-by-three-by-three is not the ultimate test. Anybody can think of that. The real world is how do you do it? How do you hold together a three-by-three-by-three?
Transcript, pp. 34-5. As reflected in the last quoted paragraph, CBS's primary argument against a finding of infringement under the doctrine of equivalents is that the means of engagement utilized in Rubik's Cube and Rubik's Revenge is materially different from, and substantially better than, the engaging means suggested in the '201 patent.[3] While I agree that the means developed by Rubik for engaging his 3x3x3 and 4x4x4 puzzles involved more creativity than that possessed by puzzle designers of ordinary skill in the art at the relevant time and contributed significantly to the appeal and commercial success of those puzzles, it does not follow that there is no infringement under the doctrine of equivalents. Claims 3 through 5 claim methods for operating a puzzle; they make no claim concerning the mechanism for holding a puzzle together.
CBS urges that the manner of engagement is relevant to our analysis for two reasons. First, it notes that in framing the questions to be addressed on remand, the Court of Appeals expressly referred to the "Rubik's puzzles with their structural differences." 793 F.2d at 1272. However, given the court's recognition of the fact that the '201 patent describes the claimed method from the perspective of the puzzle user, its earlier reference to the "structural recitation" of Claim 3 as "eight cube pieces," 793 F.2d at 1271, and its finding that the 2x2x2 Rubik's Pocket Cube literally infringed despite differences in the engaging mechanisms, we are quite confident that our mandate is limited to considering the differences between the number of apparent cubes that comprise the composite cube of each puzzle and that it does not *665 extend to an analysis of the differences in the means of engagement.
Second, CBS relies heavily on the fact that the first step of the method of independent Claim 3 calls for "engaging eight cube pieces as a composite cube." (Emphasis supplied.) The heart of CBS's oral argument was as follows:
Claim 3 says engaging eight cubes as a composite cube. So obviously [an analysis of `substantially the same way'] involves how those cubes are engaged. This is a limitation in the claim which cannot be disregarded, when viewing it from the doctrine of equivalents. That limitation must be found or its equivalent.
*   *   *   *   *   *
So what this brings into play immediately are the mechanisms by which this is done. So your Honor must then look at the mechanism and determine whether that mechanism is such from [sic] that is disclosed in the Nichols patent and what he is entitled as equivalent, whether that structure is equivalent the way it's done in Rubik's Cube and Rubik's Revenge. We believe it's very crystal-clear because of the word "engaging" that this Court must look at the mechanism involved.
Neither this Court nor the CAFC has ever looked at Claims 3 through 5 under the doctrine of equivalents. It was only done from the viewpoint of literal infringement. The test for literal infringement is totally different than for the test under the doctrine of equivalents.
Transcript, pp. 30-31. The flaw in this argument is that with respect to those elements of a claim where there is literal infringement, with one exception not here relevant,[4] analysis under the doctrine of equivalents does not differ conceptually from that required by the doctrine of literal infringement. If it were otherwise a potential infringer could put himself or herself in a materially better position with respect to the potentially infringed patent by the simple expedient of making an obvious substitution for one of the elements of the invention.
Given the holding of the Court of Appeals with respect to Rubik's 2x2x2 cube puzzles, CBS cannot seriously argue that differences in the mechanical mode of engagement of the accused puzzles is relevant to a literal infringement analysis. As CBS tacitly concedes, "engaging ... cube pieces as a composite cube" literally reads on Rubik's Cube and Rubik's Revenge. It is only the apparent number of pieces engaged as a composite cube that distinguishes the accused methods of puzzle operation from the method described in the '201 patent. Accordingly, CBS must argue that by making the obvious change in the number of apparent cubes in the composite cube, it becomes entitled to have the court reexamine, by a more rigorous standard, the issue of whether a user of Rubik's Cube or Rubik's Revenge employs a method involving "engaging ... pieces as a composite cube."
Acceptance of CBS's argument would create an anomaly in the patent law. Assume, hypothetically, that one secures a patent for a combination of elements for the harvesting of cotton consisting of (1) a tractor, (2) a large, iron, wheel mounted comb with concave teeth, and (3) a collecting receptacle. Clearly someone who developed a substantially better collecting receptacle than that taught but not claimed in the patent could not utilize it with a tractor and a large, iron, wheel mounted comb with concave teeth to harvest cotton. Such use would be barred by the doctrine of literal infringement. If CBS's analysis were correct, however, the potential infringer could avoid literal infringement by *666 making his or her comb of steel and then attempt to avoid infringement by equivalents by relying on the improved collecting receptacle. I think it unlikely that Congress intended that an obvious substitution of this kind could so improve the position of a potential infringer.
In summary, Claims 3 through 5 of the '201 patent describe methods for utilizing a composite cube puzzle. Those claims literally read on the accused device except for the number of apparent cubes comprising the composite cube and the rotating sets. Altering the number of those apparent cubes so that the sets of apparent cubes to be rotated around an axis are increased from 4 to 9 or 16 cubes does not materially alter the method which the user of the puzzle employs. The altered puzzles perform substantially the same function, in substantially the same way, to achieve substantially the same result. Although the fact that Rubik invented an improved means of holding the composite cube together may foreclose the holder of the '201 patent from practicing its invention with equivalent improved means, and although that fact may play a major role in the calculation of a reasonable royalty under the '201 patent,[5] it does not mean that CBS has not infringed method Claims 3 through 5 under the doctrine of equivalents.[6] An appropriate injunction will be entered and the issues regarding monetary recovery will be referred to the magistrate as a special master. 28 U.S.C. § 636(b)(2); Fed. R.Civ.P. 53(b).
Submit agreed upon order within fifteen days or alternative proposals within twenty days.
NOTES
[*]   Honorable Walter K. Stapleton, United States Circuit Judge for the Third Circuit, sitting by designation.
[1]  CBS also suggests in a footnote that the phrase "which pieces have constantly exposed and constantly nonexposed surfaces," does not read on Rubik's Cube or Rubik's Revenge. It notes that the Rubik's Cube and Rubik's Revenge have 26 and 56 exposed pieces respectively and that each has an internal center piece which has no constantly exposed surface. I do not agree. The only pieces referred to in the claims at issue as having constantly exposed and constantly non-exposed surfaces are those "sets of pieces" that make up the "preselected pattern." The Court of Appeals implicitly so concluded in the context of finding that the 2x2x2 Rubik's Pocket Cube literally infringed despite the fact that it too has internal, unexposed components. See 793 F.2d at 1272. Accordingly, there is literal infringement of the phrase concerning exposed and unexposed surfaces.
[2]  A jigsaw puzzle similarly increases in challenge and complexity as one divides the composite picture into more and more constituent pieces. A 200 piece jigsaw puzzle nevertheless remains the functional equivalent of a 25 piece jigsaw puzzle.
[3]  At times, CBS appears to argue not only that Rubik's engaging mechanisms are better but also that the '201 patent does not teach a method that will engage the cube pieces of a 3x3x3 or a 4x4x4 puzzle. To the extent CBS so argues, I disagree. I am satisfied that a tongue-in-groove arrangement could accomplish this task. Nevertheless, I agree that Rubik's means of engagement are far superior to anything conceived by Nichols.
[4]  The one exception is where the so-called reverse doctrine of equivalents applies, i.e., those rare cases where an element of a claim literally reads on the accused method or device but it is "so far changed in principle ... that it performs the same or a similar function in a substantially different way." Graver Tank & Mfg. Co., Inc., v. Linde Air Products Co., Inc., 339 U.S. 605, 608, 70 S.Ct. 854, 856, 94 L.Ed. 1097 (1950); SRI Intern. v. Matsushita Elec. Corp. of America, 775 F.2d 1107 (Fed.Cir.1985); 4 Chisum, Patents, § 18.04 [4]. Here it cannot be said that the methods of the user of the accused devices are so far changed in principle from the patented method that they function in a substantially different way.
[5]  For example, factor 13 of the so-called Georgia Pacific factors for consideration in establishing a reasonable royalty, see Georgia Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), modified 446 F.2d 295 (2d Cir.1971), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971), is:

The portion of the realizable profit that should be credited to the invention as distinguished from the non-patented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer.
The Georgia Pacific factors have been cited with approval by the Court of Appeals for the Federal Circuit. See, e.g., Hanson v. Alpine Valley Ski Area, Inc., 718 F.2d 1075, 1077 (Fed.Cir.1983).
[6]  I have considered CBS's file wrapper estoppel arguments and find them unpersuasive.
