▁letters ▁should ▁make ▁up ▁a ▁phrase ▁( as ▁in ▁the ▁example ▁above ). ▁ ▁Ver bal ▁arithmetic ▁can ▁be ▁useful ▁as ▁a ▁motiv ation ▁and ▁source ▁of ▁exer cis es ▁in ▁the ▁teaching ▁of ▁algebra . ▁ ▁History ▁ ▁C rypt arith mic ▁puzz les ▁are ▁quite ▁old ▁and ▁their ▁invent or ▁is ▁not ▁known . ▁An ▁ 1 8 6 4 ▁example ▁in ▁The ▁American ▁Agricult ur ist ▁dis pro ves ▁the ▁popular ▁notion ▁that ▁it ▁was ▁invent ed ▁by ▁Sam ▁Lo yd . ▁ ▁The ▁name ▁" c rypt arith m " ▁was ▁co ined ▁by ▁puzz list ▁Min os ▁( pse ud onym ▁of ▁Simon ▁V atri quant ) ▁in ▁the ▁May ▁ 1 9 3 1 ▁issue ▁of ▁S ph inx , ▁a ▁Belg ian ▁magazine ▁of ▁recre ational ▁mathematics , ▁and ▁was ▁translated ▁as ▁" c rypt ar ithmetic " ▁by ▁Maurice ▁Kra itch ik ▁in ▁ 1 9 4 2 . ▁ ▁In ▁ 1 9 5 5 , ▁J . ▁A . ▁H . ▁Hunter ▁introduced ▁the ▁word ▁" alph am etic " ▁to ▁design ate ▁crypt arith ms , ▁such ▁as ▁D uden ey ' s , ▁whose ▁letters ▁form ▁meaning ful ▁words ▁or ▁phr ases . ▁ ▁Types ▁of ▁crypt arith ms ▁ ▁Types ▁of ▁crypt arith m ▁include ▁the ▁al ph am etic , ▁the ▁dig im etic , ▁and ▁the ▁ske let al ▁division . ▁▁▁ ▁Al ph am etic ▁ ▁A ▁type ▁of ▁crypt arith m ▁in ▁which ▁a ▁set ▁of