*274Defendant Stanley Sikorski wants to build a four-bedroom, two-and-one-half story single family residence on a vacant lot (lot) in Provincetown (town). At issue is the application of § 2640 of the town zoning by-law (by-law), which regulates the scale of new construction and additions. Despite the fact that § 2640 expressly states that it "is applicable to all new buildings and all additions in all zoning districts in Provincetown," the building commissioner and zoning board of appeals (board) concluded that the by-law's proscriptions were inapplicable to the *275proposed building here. In an appeal brought by abutters Jonathan Sinaiko and Camille Cabrey (abutters) pursuant to G. L. c. 40A, § 17, a Superior Court judge upheld the board's decision on cross motions for summary judgment. The abutters now appeal, arguing that the plain language of § 2640 requires its application here, and that, as applied, the by-law requires Sikorski to seek a special permit for his proposed building. Because we agree, we reverse the judgment.

Background.3 a. The by-law. Section 2640 of the by-law regulates building scale. Its express purpose is to preserve the town's existing character of "buildings that have relatively consistent and harmonious scale within neighborhoods," and to prevent the construction of "[n]ewer buildings, where the appropriate scale has not been maintained, [that] have disrupted the character of the neighborhoods." By-law § 2640(B). To serve these ends, the by-law limits the size of new buildings and building additions that can be constructed. Those limits are keyed to the size of existing structures (measured by volume) that already exist in the relevant area.

Under the terms of § 2640 D, a landowner can-as of right-build a new structure (or expand an existing structure) that is up to twenty-five percent larger than the average size of existing buildings in the area (referred to in the by-law as the "neighborhood average").4 Under § 2640(E), a landowner can seek to construct a larger building than can be built as of right by applying for a special permit from the board. The board is vested with broad discretion to grant a special permit where "the deviation [from the scale allowed as of right] is appropriate and [the proposal] meets one or more of [six enumerated] criteria" (the specifics of which we reserve for later discussion). Ibid.

*990The details of how the neighborhood average is to be calculated are important.5 That average is set based on existing structures that lie within 250 feet of the applicable measuring point. That *276measuring point in turn varies depending on whether the proposal is for new construction or for the expansion of an existing structure. For new construction, the starting point is "the center of the parcel," while for proposed expansions it is "the center of the proposed renovation." By-law § 2640(C). Generally, all existing structures that lie within 250 feet of the applicable measuring point are to be included, with the qualification that "the largest and smallest structures" within that radius are to be excluded.6 Ibid. Thus, the neighborhood average employs a form of what statisticians refer to as a "trimmed mean." See Oxford Dictionary of Statistical Terms 412 (6th ed. 2006).

b. The proposed building. The lot in question is owned by defendant David Mayo, but Sikorski apparently has agreed to purchase it contingent on his obtaining a building permit. The lot, which is rectangular, is over one acre in size, but it is exceptionally long and narrow. Specifically, the lot is only forty-nine feet wide, but over 1,000 feet long. One of the narrow sides fronts on Bradford Street, with the lot extending north from that street deep into a wooded area.7

Sikorski originally proposed to build a two-family residence at a particular location on the lot. Because of neighborhood opposition to that proposal, Sikorski changed it to a single-family home, reduced its size, moved its location on the lot, and modified its design in certain respects. Under the revised proposal, the building would remain a not insubstantial structure. For example, the building will include two-and-one-half stories8 -the maximum allowed in the town9 -and comprise 33,810 cubic feet in volume.

*27710

The proposed house is to be located at the southern edge of the lot, that is, next to Bradford Street. It is undisputed that there are many existing structures in close proximity to that proposed location. For example, as the abutters pointed out in their appeal to the board, there are approximately sixteen structures that lie *991within 250 foot of the center of the proposed building, and the average volume of those structures-not including the largest and smallest-is 9,250 cubic feet. Thus, the proposed building is over three times larger than what the neighborhood average would have been if that figure were calculated using the actual location of the proposed structure.

As noted, however, the neighborhood average for new construction is to be calculated based on the center of the lot, not where the proposed building is in fact to be located. Because of the relatively unusual shape of the lot here, that difference has a significant effect. There are only two existing buildings that lie within 250 feet of the center of the lot. Those structures have volumes of 8,200 and 4,560 cubic feet, respectively. Thus, if the ordinary mean of those two structures were used (6,380 cubic feet), the proposed structure would be over five times as large (a disparity in scale even greater than if the actual location were used).

Excluding the two nearby structures from the calculation-based on their being considered the largest and the smallest of the structures lying within 250 feet of the center of the lot-left no existing structures on which to base a neighborhood average. This presented town officials with the conundrum of how to calculate the neighborhood average here. As evidenced by a "scratch out" on the relevant form, an assistant assessor for the town initially calculated the neighborhood average as zero.11 However, apparently upon further reflection, he concluded that the neighborhood average simply was "N/A," which the parties agree is shorthand for "not applicable." Under this interpretation, § 2640 placed no constraints on the size of building that Sikorski could build as of *278right. The building commissioner relied on this interpretation in determining that a building permit should issue.

On an appeal brought by the abutters, the board affirmed. While acknowledging that § 2640 was required "to be applied to all new buildings," the board concluded that in the circumstances of this case, "there [was] no scale calculation procedure to follow." The board also stated that it had taken into consideration that Sikorski had redesigned his original proposal to reduce its scale "in response to previous neighbor objections."

On cross motions for summary judgment, a Superior Court judge affirmed the board's decision. He reasoned that § 2640 was ambiguous because it did not address how the neighborhood average was to be calculated in the circumstances of this case. He then observed that the by-law's purpose was to "maintain consistent scale among existing buildings," and that it did not reference "preserving undeveloped land in its natural state." Finally, he concluded that in light of this intent, "it [was] reasonable for the [b]oard to conclude that where no qualifying structures exist in the 250 foot radius, there is no existing scale which must be protected."

Discussion. To help frame the analysis that follows, we begin with some preliminary observations. It is important to keep in mind that the abutters make two different arguments. The first is that the board's interpretation of § 2640 is invalid because it is at odds with that section's plain language and otherwise unreasonable. The second is that their own proffered interpretation (under which the neighborhood average here had to be taken as zero) must be accepted. These contentions, while related, are conceptually distinct. As elucidated below, it is possible to conclude that the interpretation offered *992by the board is untenable without concluding that the abutters' particular counter interpretation necessarily is required.

Overall, this case raises two inquiries. One is whether the building scale by-law applies. The other is, if so, how it applies (that is, how the neighborhood average here should be determined). The first question is addressed by the plain language of the by-law, which begins with the edict that the by-law "is applicable to all new buildings and all additions in all zoning districts in Provincetown."12 By-law § 2640(A). That language is binding on the board, and the board therefore is not free to determine *279that the by-law simply is inapplicable. See MacGibbon v. Board of Appeals of Duxbury, 356 Mass. 635, 640, 255 N.E.2d 347 (1970) (board of appeals could not adopt interpretation of by-law where its plain language provided "no basis for such an interpretation"). Cf. Warcewicz v. Department of Envtl. Protection, 410 Mass. 548, 550, 574 N.E.2d 364 (1991) ("[C]ourts will not hesitate to overrule agency interpretations [of their own regulation] when those interpretations are arbitrary, unreasonable, or inconsistent with the plain terms of the regulation itself").

Having resolved that § 2640 applies, we now turn to the second inquiry: how the neighborhood average is to be calculated in the circumstances presented. As noted, the board concluded that the by-law places no limits on the proposed building's size. As the abutters point out, having rejected a neighborhood average of zero, the board effectively set that average at infinity instead.

The results of the board's interpretation are highly anomalous: how can it be that a proposed new building is exempt from regulation under a generally-applicable building scale by-law no matter how large that building would be? In addition, by exempting a structure that in fact grossly exceeds the scale of other buildings in the area, the board's interpretation flies in the face of the by-law's directive that "[a]ll new buildings or additions shall comply with appropriate scale to their neighborhood." By-law § 2640(B). Even to the extent that the judge was correct that the by-law is ambiguous with regard to how the neighborhood average should be interpreted in the circumstances of this case, the board's resolution of that ambiguity was not reasonable. See Britton v. Zoning Bd. of Appeals of Gloucester, 59 Mass. App. Ct. 68, 72, 794 N.E.2d 1198 (2003), quoting from MacGibbon v. Board of Appeals of Duxbury, 356 Mass. at 639, 255 N.E.2d 347 (zoning board decision will be overturned if "based on a legally untenable ground or it is unreasonable, whimsical, capricious or arbitrary"). See also Pelullo v. Croft, 86 Mass. App. Ct. 908, 909, 18 N.E.3d 1092 (2014) ("[A]court owes deference to the interpretation of a zoning by-law by local officials only when that interpretation is reasonable").13

*993*280In contrast, the abutters' alternative interpretation is based on an arguably straightforward application of the by-law's language: where there are no buildings in the relevant neighborhood, the neighborhood average is zero. Moreover, their interpretation does not mean that Sikorski necessarily will be unable to build his desired house, but only that he will have to seek a special permit to do so. The by-law delegates to the board broad discretion to grant case-by-case exemptions from the by-law's strict application.14

At the same time, the abutters' interpretation produces its own anomalies. How can it be, for example, that a landowner who has proposed to construct a new structure in an area populated by numerous other existing structures nevertheless be burdened by a neighborhood average of zero (and thereby be forced to seek a *281special permit) no matter how small his proposed structure may be? In addition, as a matter of mathematics, trying to divide zero by zero is an endeavor destined to produce an indeterminate result.

Thus, it is apparent that if the board's available choices for setting the neighborhood average were limited to zero and infinity, there are anomalies either way. That realization should have caused the town officials to question whether they were limited to these two problematic options. In other words, could there be a third interpretation that better fit with both the letter and intent of the by-law? Cf. Reade v. Secretary of the Commonwealth, 472 Mass. 573, 578, 36 N.E.3d 519 (2015), quoting from Watros v. Greater Lynn Mental Health & Retardation Assn., 421 Mass. 106, 113, 653 N.E.2d 589 (1995) ("[I]t is a well-established canon of statutory construction that a strictly literal reading of a statute should not be adopted if the result will be to thwart or hamper the accomplishment of the statute's obvious purpose, and if another construction which would avoid this undesirable result is possible"). One does not have to look far to find such an interpretation.15

*994Here, the building commissioner ended up with no existing structures on which to determine a neighborhood average only because he excluded the two existing structures that in fact are located within 250 feet of the center of the lot. The obvious question is whether the terms of § 2640 required him to do so. The only apparent reason for the by-law's relying on a trimmed mean instead of an ordinary "arithmetic mean" is to try to avoid the problem of outliers unduly skewing the resulting average. See Oxford Dictionary of Statistical Terms 412 (idea of trimmed mean is "[to reduce] the sensitivity of the arithmetic mean to extreme observations").16 In other words, excluding values at either end is done based on the theory that doing so may yield a more representative center value. Here, the exclusion of the only two available data points had the opposite result: it left a null set, which in turn presented town officials with having to choose between zero and infinity as the operative neighborhood average.

*282Nothing in the language of § 2640 compelled the building commissioner to exclude existing structures when doing so would leave him without a basis upon which to set a neighborhood average.17 In fact, the specific language of the by-law cuts in the other direction. That is because the terms "largest" and "smallest" that appear in the by-law properly are used only in relation to three or more items (for two items, "larger" and "smaller" would be proper). See by-law § 2640(C); Chicago Manual of Style § 5.86, at 253 (17th ed. 2017) ("A superlative adjective expresses the relationship between at least three things and denotes an extreme of intensity or amount in a particular shared quality"). Thus, under a grammatically correct reading of the by-law's plain language, the directive that the building commissioner exclude the "largest" and "smallest" structures in calculating a neighborhood average would apply only where there are three or more structures within 250 feet of the applicable measuring point. See generally Commonwealth v. Wright, 88 Mass. App. Ct. 82, 86, 36 N.E.3d 569 (2015) ("In interpreting legislation, we employ familiar canons of statutory and grammatical interpretation"). Applying such an interpretation here, the two structures within 250 feet of the applicable measuring point would not be excluded in calculating the neighborhood average.

Conclusion. In sum, we agree with the abutters both that the by-law applies to the proposed building and that the board unreasonably interpreted how it applies. Although the particular counter-interpretation proposed by the abutters has its own problems, there is at least one interpretation of the by-law that accords with both its language and express purpose.18 The proposed building is too large *995to be approved under that interpretation without a special permit.19 With none of the defendants having offered a reasonable interpretation of the by-law under which the *283proposed building could be constructed as a matter of right, we reverse the judgment. A new judgment shall enter in favor of the abutters.20

So ordered.