# Talk:Palindromic gapful numbers

## Please clarify[edit]

I don't understand the second and third part of the requirements. What does this mean?

- Show (nine sets, like above) of palindromic gapful numbers:

- the last 15 palindromic gapful numbers (out of 100)
- the last 10 palindromic gapful numbers (out of 1,000) {optional}

Thanks. --Paddy3118 (talk) 19:54, 12 November 2019 (UTC)

- Is it:
*The last fifteen of the first 100 binned-by-last digit gapful numbers >= 100*

- --Paddy3118 (talk) 19:59, 12 November 2019 (UTC)

Starting at **100** (which is the minimum that gapful numbers start at, as per the note on the task page that all positive integers below **100** are trivially gapful numbers), then ...

- generate
**100**palindromic gapful numbers, and then take (pick) the last**15**of those**100**numbers. - generate
**1000**palindromic gapful numbers, and then take (pick) the last**10**of those**1000**numbers.

- generate

There is probably a better and cleaner (or more concise) way of expressing the above (two) sentences, but the (bottom/lower) limit of **100** kinda throws a monkey wrench into the works, er ... wording of the expression.

Another way of expressing the above would be:

- generate the
**86**──►^{th}**100**palindromic gapful numbers, ignoring those below^{th}**100**. - generate the
**991**──►^{st}**1000**palindromic gapful numbers, ignoring those below^{th}**100**.

- generate the

I had assumed that programmers would take/pick those (above) palindromic gapful numbers in increasing order, and it seemed unnecessary to state that.

I must admit, I never heard of that phrase *binned by last*, but once reading it, I knew what it meant.

I hope the parenthetic phrase **(nine sets)** was clear enough; If it wasn't for the output, I don't know how I would've expressed it. I assumed the output from the REXX example would make that clear enough. I had toyed with expanding that parenthesized expression, but it just got too overly wordy and inelegant, and even somewhat ugly. -- Gerard Schildberger (talk) 00:12, 13 November 2019 (UTC)

- Hi Gerard, as you saw above, I did eventually work it out.
- Having looked again at my wording I think it might be better with an extra hyphen tieing in the word "digit"?
*The last fifteen of the first 100 binned-by-last-digit gapful numbers >= 100*

- --Paddy3118 (talk) 20:16, 13 November 2019 (UTC)
- P.S. I enjoyed the task.

## optimizations[edit]

(Referencing Paddy3118's comment above.)

I thought it was a pretty simple task, nothing much complicated, but enough computation so that it required just a hint of heavy lifting (at least, for the solution I entered). I thought I hit on a clever method to limit the calculation (to ten) entries per ending decimal digit without computing extra entries or excessive limit checking.

It was interesting to note some of the optimizations for this task, ... which to do first ... create palindromes and then filter the gapful numbers, or vice-versa. -- Gerard Schildberger (talk) 20:52, 13 November 2019 (UTC)