# The Final Pathetic Bleatings of the Forum

Question:

I am ver ashamed of all of you panelists for making all
of those blond jokes. I have blond hair and I am not stupid
at all. Math is NOT hard. What's up with all the blond
jokes? Jerks!

Replies:

I eventually gave up on using the needlenose and stripped it with my teeth.

You think you're so smart eh? Well, it looks like SOMEONE needs a little math quiz.

If you are so smart, solve the following problems.

What is the prime factorization of 3497576788779231956999997230425066955980440596678055687539811268032443620834988600137130693596447083940141497556283255152769544840335367814320577922754068111937835484054976193999260548148079539917979400332539028396871875450262100400906906148670856815055241776429734100396915959053017918557040556924855975210396246131479832945523765555178603209790081561134660045420812499474624541692981943847500481804869038385646022775793608901196651849887507534897071840768367008974671557861930929127194082018437809737889680658532729848481519575786471928098931500407538644787278963726332362530089113481273709419115150029998191277213002948124916356322467085223096585411185649194319366061590331606837720471271491198122665590572431498001120398366827597194431637880372045216392086601161926115065809135332408220751661282795935618599028244929353898667546678388658234332683363790756121777853745135210848086566682734417368715623073372641854665752114454762223165932158825314356620853885303595882411547803146997634468133305812152254438114703807417490613763418268649185957365839487144702569994684241349328064960532261089817640492049199892433894541143141942709347671884458161151686102066872452048589562522058839576385807393843618751289238149389797479431756923083902550641199937792662058966136329707005742749293122957180925487694705242613732785790172552822828804886208345407006121753336606985503031723017017778626000797032230334664143380049281809982702485767865492816119524294639211847939981485622760631434816992782287944858402875404902404369245941614917781870818610713338034415628184215646551801968328327470697223219679629675592056447310507114297282560332691876214575399033354583682627152748638764700135270708977347293922009427871606508211519675623835713722174657031860623663112397529420551688285012539718334657608688667183303239388089330184149525101862338664197828720485420708154525783181702474733567066003591820204028163363486741274810336003208196201569861368318685740451040261898617731093258493613799032150307041291975914612051927440080634147571789868033669213063735950588174937885451041823120424683023662480625177640560708453079711743?

Ah, you are not worth it.

Prove false.

Show that there is a power of 2 whose last 1000 digits are all 1's and 2's.

Prove that every positive integer can be written as the sum of not more than 53 fourth powers of integers.

Prove that every positive rational number (in particular, every positive integer) can be written as the sum of three cubes of positive rational numbers.

Prove that if the legs of right-angle triangle are expressible as the squares of integers, the hypothenuse cannot be an integer.

Rearrange the integers from 1 to 100 in such an order that no eleven of them appear in the rearrangement (adjacently or otherwise) in either ascending or descending order.

Prove that no matter what rearrangement is made with the integers from 1 to 101 it will always be possible to choose eleven of them which appear (adjacently or otherwise) in the arrangement in either an ascending or descending order.

A chess master who has eleven weeks to prepare for a tournament decides to play at least one game every day, but in order not to tire himself he agrees to play not more than twelve games during one week. Prove that there exists a succession of days during which the master will have played exactly twenty games.

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