Compressing the ends of the cylinder, the extension disappears and we isolate a remnant plane. This is analogous to eliminating the high-end of a price range.

*Resuggesting to improve range and to update mini with an additional sale.*

Sales:

1. Sale no. 1

+ 4 Keys, sold for Circling TF Logo Bonk Helm (15 Keys)

Result: 15 - 4 Keys = 11 Keys

Note: Beanie was offered on the Bonk Helm, so no overpay needs to be calculated..



2. Sale no. 2

Sold for 12 Keys pure.

Proof: [url]http://imgur.com/pPHUJsz[/url]



3. Sale no. 3

Sold for a Disco Beatdown Electric Escorter (15 Keys) - Mini provided

Result: 15 * 0.9 Keys = 13.5 Keys, rounding down to 13 Keys

Note: Downplaying the other sale in the mini, which was for pure at ~10 Keys, but was outdated by 3 months, preceding the obsolescence of Buds as a currency.




Backpack of seller before: [url]http://backpack.tf/profiles/76561197969363424?time=1434870000[/url]

Backpack of seller after: [url]http://backpack.tf/profiles/76561197969363424?time=1434956400[/url]

Note: Circling Peace Sign Beanie does not show in the historical view of the seller's backpack, but is evidenced in the history of the Unusual.




Backpack of buyer before: [url]http://backpack.tf/profiles/76561198103060345?time=1434870000[/url]

Backpack of buyer after: [url]http://backpack.tf/profiles/76561198103060345?time=1434956400[/url]



4. Mini for Electric Escorter

1. Seems to have sold for a Bud (~March 26, 2015) when Buds were 9.5 Keys according to the spreadsheet.

Note: At this time, Unusual prices were still in Buds, which was until recently a form of currency. Original price of the Escorter was 1.1 Buds, which is consistent with this particular sale. The reversion to Keys occurred on April 1, 2015 (decidedly not a joke). May be outdated.




Bud history: [url]http://backpack.tf/item/92860070[/url]

Backpack of buyer before: [url]http://backpack.tf/profiles/76561198036287213?time=1426143600[/url]

Backpack of buyer after: [url]http://backpack.tf/profiles/76561198036287213?time=1426143600[/url]




2. Sold for a Kill-a-Watt Stately Steel Toe (15 Keys)

Note: Steel Toe was offered on the Beanie, so no overpay needs to be calculated.

Backpack of buyer before: [url]http://backpack.tf/profiles/76561198071995112?time=1435302000[/url]

Backpack of buyer after: [url]http://backpack.tf/profiles/76561198071995112?time=1435388400[/url]

Note: This sale is more recent and will take precedence over the pure sale.

Taking a range of 11 - 13 Keys, unless additional sales surface that contradict this range, thereby necessitating a readjustment. Lower than I expected, but that possibly reflects the gradual decay of the Unusual economy. Seems about right.