RNGdle Sandwich Badge: Matching Ends and Number Count

The original condition and value

The original Sandwich badge page says “First and last digits match, with at least one different digit between them.” It listed Uncommon, 1,000 EP and 10.0% probability when checked September 24, 2026. This is a badge value, not the total EP or rarity of every result that earns it.

Under the sentence’s ordinary decimal reading, 121 has matching ends and a different middle digit; 111 has matching ends but no different digit between them; 123 has different ends. These illustrate the written rule, not observed badge awards. The original result remains the authority for a specific number.

How many integers fit the written condition?

The original About page says the roll range is 0 through 1,000,000. For a decimal number with d digits from 3 through 6: choose one of 9 nonzero first digits; the last digit must match it; choose any of 10^(d−2) middle strings except the one where every middle digit also matches. That gives 9 × (10^(d−2) − 1) candidates at each length.

Digits	Count under the written rule
3	81
4	891
5	8,991
6	89,991
Total	99,954

One- and two-digit numbers have no different interior digit; the only seven-digit value in the stated range is 1,000,000, whose ends do not match. So 99,954 of 1,000,001 integers, or about 9.9954%, fit this literal reading. That rounds to the page’s 10.0% display. This count is our reproducible arithmetic, not a published game count or a cloned badge detector. An undocumented evaluator boundary could differ; use the live result to confirm an actual award.

Rarity and version

The About page defines badge rarity by occurrence chance and whole-roll rarity by total EP. A Sandwich badge’s Uncommon label does not imply the roll itself is Uncommon; see EP and rarity.

The published changelog gives no Sandwich introduction or rule revision in its recent entries and says earlier history is incomplete. We have checked the current badge page, not established an unchanged rule across all versions. Recheck the page if the condition or value changes.

Source and scope: original Sandwich badge, About, Changelog, checked September 24, 2026. See other verified badges. Correction channel status.