# Winning the Lottery

Bob: I hear you won the lottery.

Alice: So I did!

Bob: What six numbers did you win it with?

Alice: Can't remember. All I recall is that they were all different, and none greater than 28.

Bob: Anything else?

Alice: Yes. I checked that no other six different numbers, none greater than 28, have the same common factor graph as mine.

(The common factor graph of a set of integers is the graph whose vertices are the integers, two of which are joined by an edge if they have a common factor greater than 1.)

What six numbers did Alice win the lottery with?

$$10, 14, 15, 20, 21, 28$$
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3266255557537079, "perplexity": 631.2566239597444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655890157.10/warc/CC-MAIN-20200706073443-20200706103443-00105.warc.gz"}