Mark Gritter (markgritter) wrote,
Mark Gritter
markgritter

License Plate Vocabulary

mrissa introduced me to a simple license-plate game: given a three-letter license plate, is there a word which uses those three letters in that order?

I've been curious what percentage of possible three-letter combinations have no solution. (A somewhat harder question is what percentage of valid license plate combinations have no solution, as the selection is usually not truly random.)

Using SOWPODS as my word list, I discovered tonight that 1385 three-letter groups have no words. That is approximately 7.9% of the 17,576 possibilities.

Here's the complete list of letters with no matching words:

AJQ AJZ AKQ AQJ AQQ AQX AVJ AWJ AWQ AXJ AXQ BDJ BFJ BFQ BGJ BGQ BGX BHQ BJJ BJQ BKQ BKX BMJ BMQ BPQ BPX BQF BQJ BQK BQP BQQ BQV BQW BQX BQZ BVJ BVQ BVW BWQ BXJ BXQ BXV BXX BYJ BYQ BZJ BZX CDQ CFJ CGJ CJJ CJQ CJZ CKQ CQJ CQX CVJ CWJ CWQ CXJ CXK CXQ CYJ CZJ CZX DBJ DBQ DCJ DFJ DFQ DGJ DHJ DJF DJJ DJQ DJZ DKJ DKQ DKX DPJ DQH DQJ DQP DQQ DQX DQZ DUJ DVJ DVQ DVX DWJ DWQ DXJ DXK DXQ DXV DXX DYJ DYQ DZJ DZQ DZW EFJ EJJ EJQ EJX EKJ EKQ EKZ EQJ EWJ EWQ EYJ EYQ EZJ FBQ FCJ FCQ FDJ FDQ FFJ FFQ FGQ FGX FHJ FHQ FHX FJB FJF FJH FJJ FJP FJQ FJV FJW FJX FJZ FKJ FKQ FKX FKZ FMJ FMQ FPQ FQF FQH FQJ FQK FQM FQP FQQ FQW FQX FQZ FSJ FSX FTJ FVJ FVK FVQ FVZ FWJ FWQ FWW FXJ FXQ FXW FXX FXZ FYJ FYQ FYX FZF FZH FZJ FZQ FZU FZV FZW FZX GBJ GBQ GCJ GEJ GFJ GGJ GHQ GJB GJF GJJ GJQ GJV GJW GJX GJY GJZ GKB GKF GKJ GKQ GKV GKW GKX GKZ GLJ GQB GQF GQG GQH GQJ GQK GQM GQP GQQ GQV GQW GQX GQZ GSJ GVF GVJ GVQ GWJ GWQ GXB GXC GXD GXF GXH GXJ GXK GXM GXP GXQ GXR GXU GXV GXW GXX GXZ GZJ GZQ GZV GZX HCJ HFJ HFQ HJF HJQ HJV HJW HJX HJY HJZ HKJ HKQ HPQ HQF HQJ HQV HQX HQZ HSJ HVJ HVQ HVX HWQ HXJ HXQ HXW HXX HZJ HZQ HZW HZX IFJ IJJ IJQ IJZ IKQ IQJ IQW IQX IVJ IWJ IWQ IWX IXJ IXQ IXX IZJ IZQ JBF JBJ JBP JBQ JBV JCX JDF JDJ JDQ JDX JFJ JFK JFP JFQ JFW JFX JFZ JGQ JGX JHJ JHQ JHV JHX JHZ JIQ JJC JJF JJJ JJK JJQ JJV JJW JJX JJZ JKQ JKZ JLJ JLQ JLX JMQ JMV JPQ JPV JPX JQB JQC JQF JQH JQJ JQK JQM JQO JQP JQQ JQV JQW JQX JQZ JRJ JSJ JSQ JSX JTJ JTQ JUQ JVB JVF JVH JVJ JVK JVP JVQ JVV JVW JVX JWJ JWQ JWV JWZ JXB JXC JXF JXH JXJ JXK JXM JXQ JXR JXU JXV JXW JXX JXZ JYJ JYQ JYZ JZC JZF JZH JZJ JZP JZQ JZV JZW JZX KAQ KBQ KBV KCJ KCQ KCZ KDQ KDX KEQ KFJ KFQ KFV KFX KFZ KGJ KGQ KGX KGZ KHQ KHX KIQ KJF KJJ KJQ KJV KJX KJZ KKQ KLQ KMF KMV KMX KNQ KOQ KPQ KPV KPZ KQB KQC KQD KQE KQF KQG KQH KQI KQJ KQK KQL KQM KQN KQO KQP KQQ KQR KQV KQW KQX KQY KQZ KRQ KSJ KSQ KSX KTQ KUX KVB KVF KVJ KVQ KVW KVX KWJ KWQ KXA KXB KXC KXF KXH KXJ KXK KXL KXP KXQ KXT KXU KXV KXW KXX KXZ KYQ KZF KZP KZQ KZV KZW KZX LJJ LJQ LJX LJZ LKQ LQJ LQP LQQ LQX LVJ LVQ LWQ LXJ LXQ LXW LXX LYJ LYQ LZF LZJ LZQ LZV LZW LZX MFJ MJB MJJ MJQ MJX MJZ MKQ MQB MQF MQJ MQP MQQ MQW MQX MVF MVJ MVQ MWJ MWQ MWX MXJ MXK MXQ MZX NBQ NFJ NJJ NJQ NJZ NKQ NKX NLJ NQJ NQQ NQW NQX NVJ NWJ NWQ NXJ NXQ NXW NXX NYQ NZJ NZX OFJ OHJ OJJ OJQ OKQ OQJ OQQ OQX OWQ OXJ OXQ OYJ OYQ OZJ OZQ OZV OZW OZX PBJ PBQ PCJ PDQ PFJ PFQ PGJ PGQ PJF PJJ PJQ PJW PJX PKJ PKQ PKZ PQB PQH PQJ PQM PQP PQQ PQV PQX PQZ PVJ PVQ PWJ PWQ PXJ PXQ PZJ PZQ PZV QBF QBJ QBP QBQ QBV QBW QBX QBZ QCJ QCW QCZ QDJ QDQ QDW QEJ QFJ QFK QFP QFQ QFX QFZ QGB QGF QGJ QGK QGP QGQ QGV QGW QGX QGZ QHF QHH QHJ QHK QHV QHX QHZ QJB QJC QJD QJE QJF QJG QJH QJI QJJ QJK QJL QJM QJN QJO QJP QJQ QJR QJT QJU QJV QJW QJX QJY QJZ QKC QKF QKJ QKQ QKU QKW QKX QKZ QMJ QMK QMW QMX QMZ QNJ QNW QOJ QPF QPJ QPK QPQ QPV QPW QPZ QQB QQJ QQK QQQ QQW QQX QQZ QRJ QRQ QSJ QSK QSQ QSX QSZ QTJ QTQ QVJ QVP QVW QVX QVZ QWC QWJ QWP QWQ QWV QWX QWZ QXB QXF QXH QXJ QXK QXP QXQ QXU QXV QXW QXX QXZ QYF QYH QYJ QYO QYP QYQ QYU QYV QYW QYX QYZ QZH QZJ QZK QZP QZQ QZV QZW QZX RFJ RJJ RJQ RJX RKQ RLJ RQJ RQQ RQW RQX RVJ RWJ RWQ RXF RXJ RXK RXQ RXW RXX RZJ RZQ RZX SFJ SFQ SGQ SJJ SJQ SJX SKQ SQJ SQQ SWQ SXJ SXQ SXW SZJ SZQ SZX TBQ TFJ TJF TJH TJJ TJQ TJZ TKQ TKZ TQB TQF TQH TQJ TQP TQQ TQV TQW TQX TVJ TVQ TVX TWQ TXJ TXQ TXX TZX UFJ UGJ UHJ UJJ UJQ UKQ UQJ UQQ UQW UQX UVJ UWJ UWQ UXJ UXK UXQ UXW UXX UYQ UZQ UZV UZX VBQ VCJ VCQ VDQ VFJ VFP VFQ VFX VGJ VGK VGQ VGX VHJ VHX VIJ VJB VJF VJH VJJ VJK VJQ VJV VJX VJZ VKC VKF VKJ VKQ VKU VKW VKX VLJ VMJ VMW VNJ VOJ VPJ VPQ VQJ VQQ VQV VQW VQX VSJ VTJ VUJ VUQ VVJ VVQ VWJ VWQ VWV VWW VWX VXF VXJ VXK VXQ VXW VXX VXZ VYF VYJ VYQ VYV VYX VZJ VZQ VZV VZW VZX WBJ WBQ WBV WCJ WCQ WDQ WFJ WFQ WFV WFX WFZ WGJ WGQ WGX WHQ WIQ WJD WJF WJH WJJ WJQ WJV WJW WJX WJY WJZ WKJ WKQ WKZ WLQ WMJ WMQ WMX WNQ WOJ WOQ WPQ WQB WQC WQD WQG WQH WQI WQJ WQL WQM WQN WQO WQP WQQ WQR WQT WQV WQW WQX WQY WQZ WSJ WSQ WSX WUQ WUV WVJ WVQ WVV WVX WVZ WWJ WWQ WWZ WXJ WXQ WXU WXV WXX WXZ WYJ WYQ WYX WZF WZH WZJ WZP WZQ WZV WZW WZX XAQ XAW XBF XBJ XBP XBQ XBX XCF XCJ XCW XDF XDJ XDK XDQ XDX XEJ XFJ XFK XFP XFQ XFX XFZ XGJ XGK XGQ XGW XGX XHF XHJ XHW XIJ XIQ XJB XJE XJF XJG XJH XJJ XJK XJM XJN XJO XJP XJQ XJR XJS XJT XJV XJW XJX XJZ XKB XKC XKF XKG XKJ XKK XKM XKQ XKU XKV XKW XKX XKY XKZ XLJ XLQ XLX XMJ XMQ XMW XMX XNJ XNQ XNW XOJ XOQ XPJ XPQ XPX XQB XQC XQF XQH XQJ XQK XQM XQO XQP XQQ XQV XQW XQX XQZ XRQ XSJ XSQ XSX XTQ XUJ XUK XUQ XUW XVB XVF XVJ XVK XVP XVQ XVW XVX XWB XWC XWF XWJ XWP XWQ XWT XWU XWV XWW XWZ XXB XXF XXH XXJ XXK XXM XXO XXP XXQ XXR XXV XXW XXX XXZ XYJ XYK XYQ XYV XYW XYX XZC XZF XZH XZJ XZK XZQ XZU XZV XZW XZX XZZ YAJ YBJ YBV YCJ YCQ YDJ YEJ YFJ YFP YFX YFZ YGJ YGQ YGX YHJ YIJ YJB YJF YJH YJJ YJL YJO YJP YJQ YJT YJU YJV YJW YJX YJY YJZ YKB YKJ YKP YKQ YKV YKX YLJ YMJ YNJ YPJ YQB YQF YQH YQJ YQM YQP YQQ YQV YQW YQX YQZ YRJ YSJ YUJ YUW YVB YVF YVJ YVK YVM YVP YVQ YVV YVW YVX YWJ YWQ YWU YWV YWX YWZ YXF YXJ YXQ YXW YXX YYF YYJ YYK YYQ YZF YZH YZJ YZK YZP YZQ YZW YZX ZBP ZBQ ZBV ZBX ZCJ ZCQ ZCV ZCW ZCX ZDF ZDJ ZDW ZDX ZEQ ZFB ZFJ ZFK ZFP ZFQ ZFV ZFW ZFX ZFZ ZGJ ZGQ ZGV ZGX ZHF ZHH ZHJ ZHQ ZHV ZHW ZJB ZJC ZJD ZJF ZJG ZJJ ZJL ZJQ ZJV ZJW ZJX ZJY ZJZ ZKB ZKJ ZKL ZKQ ZKW ZKX ZKZ ZLQ ZMJ ZMQ ZMX ZNQ ZNV ZNW ZOJ ZPF ZPJ ZPQ ZPV ZPW ZPX ZPZ ZQA ZQB ZQC ZQD ZQF ZQG ZQH ZQJ ZQK ZQL ZQP ZQQ ZQR ZQV ZQW ZQX ZQY ZQZ ZRJ ZRQ ZSB ZSJ ZSQ ZSW ZSX ZTJ ZTQ ZTW ZUQ ZVB ZVF ZVJ ZVK ZVL ZVM ZVP ZVQ ZVR ZVV ZVW ZVX ZVZ ZWF ZWJ ZWL ZWP ZWQ ZWV ZWW ZWX ZXB ZXD ZXF ZXG ZXJ ZXK ZXO ZXP ZXQ ZXR ZXV ZXW ZXX ZXZ ZYF ZYJ ZYK ZYQ ZYX ZZJ ZZQ ZZX

The python script I wrote scans the word list in a single pass, and keeps a tree of three-letter groups not yet found. My hope was that this would allow us to prune the generation of combination from words--- if we already know that all ABx are present we don't need to work through the remaining six letters in ABSOLUTE (similarly for ASx, ALx, etc.) But I'm not sure how big of a difference this actually makes. Guess I should have kept stats. ;)
Tags: games, geek, programming
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