2023年6月24日发(作者：)

USAAIME2002I1Manystatesuseasequenceofthreelettersfollhateachthree-letterthree-digitarrangementisequallylikely,theprobabilitythatsuchalicenseplatewillcontainatleastonepalindrome(athree-letterarrangementorathree-digitarrangementthatreadsthesameleft-to-rightasitdoesright-to-left)ism/n,+n.2Thediagramshowstwclesaretaioofthelongerdimensionoftherectangletotheshorterdimensioncan1√bewrittenas(p−q),+q.2[img]6601[/img]rs,wherenisapositiveinteger,Dick’sageandJane’sagewillbothbetwo-digitnumberandwillhavethepropertythatJane’sageisobtainedbyinterchangingthedigitsofDick’Dick’yorderedpairsofpositiveintegers(d,n)arepossible?4Considerthesequencedefinedbyak=1fork≥hatam+am+1+···+an−1=k2+k1/29,forpositiveintegersmandnwithm|y|,(x+y)r=xr+rxr−1+r(r−1)r−22r(r−1)(r−2)r−33xy+xy+···23!Whatarethefirstthreedigitstotherightofthedecimalpointinthedecimalrepresentation