Write the Rules Before Comparing Two Numbers

121 is a square and a decimal palindrome; 125 is a cube. Which is more special? Intuition can support either answer. A comparison that another person can reproduce needs explicit rules.

First ask which patterns each number satisfies. Then ask which score is higher under the same scoring system. These are different questions: properties describe the inputs, while a score expresses the weights chosen by a particular tool. A higher score does not make one mathematical property more valuable.

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Its current range includes every integer from 0 through 1,000,000, and it checks 31 named patterns. Before comparing two inputs, record both numbers. Then record their labels, scores, and range percentages. Avoid replacing an input just because the result does not match a prediction. If you choose a new pair, start a new record.

Counting labels is not enough. Some properties overlap, so another label may not provide independent information. RNGDLE groups scoring signals and discounts later signals within a group. This reduces repeated contributions; it does not establish independence or turn the total score into a joint probability.

The displayed percentage answers a separate question: how many integers in the full range have a score greater than or equal to the chosen score? The denominator is 1,000,001. Ties are included in the numerator. A smaller percentage means fewer integers reach that threshold. It does not order equal-scoring numbers, and it is not the probability of drawing that specific integer next.

After recording the comparison, change just one condition: add one to an input and repeat the same process. An unchanged result is useful too. It shows that the score does not distinguish every property. Finish with a precise conclusion: which score was higher under these rules, which labels differed, and which questions the score did not answer.