▁words ▁is ▁written ▁down ▁in ▁the ▁form ▁of ▁a ▁long ▁addition ▁sum ▁or ▁some ▁other ▁mathematical ▁problem . ▁The ▁object ▁is ▁to ▁replace ▁the ▁letters ▁of ▁the ▁alphabet ▁with ▁decimal ▁digits ▁to ▁make ▁a ▁valid ▁arithmetic ▁sum . ▁Dig im etic ▁ ▁A ▁crypt arith m ▁in ▁which ▁digits ▁are ▁used ▁to ▁represent ▁other ▁digits . ▁S ke let al ▁division ▁ ▁A ▁long ▁division ▁in ▁which ▁most ▁or ▁all ▁of ▁the ▁digits ▁are ▁replaced ▁by ▁symbols ▁( us ually ▁a ster is ks ) ▁to ▁form ▁a ▁crypt arith m . ▁Re verse ▁crypt arith m ▁ ▁A ▁rare ▁variation ▁where ▁a ▁formula ▁is ▁written , ▁and ▁the ▁solution ▁is ▁the ▁corresponding ▁crypt arith m ▁whose ▁solution ▁is ▁the ▁formula ▁given . ▁ ▁Sol ving ▁crypt arith ms ▁Sol ving ▁a ▁crypt arith m ▁by ▁hand ▁usually ▁involves ▁a ▁mix ▁of ▁dedu ctions ▁and ▁exhaust ive ▁tests ▁of ▁possibilities . ▁ ▁For ▁instance ▁the ▁following ▁sequence ▁of ▁dedu ctions ▁solves ▁D uden ey ' s ▁S END + MO RE ▁= ▁M ONE Y ▁puzz le ▁above ▁( columns ▁are ▁number ed ▁from ▁right ▁to ▁left ): ▁ ▁From ▁column ▁ 5 , ▁M ▁= ▁ 1 ▁since ▁it ▁is ▁the ▁only ▁carry - over ▁possible ▁from ▁the ▁sum ▁of ▁two ▁single ▁digit ▁numbers ▁in ▁column ▁ 4 . ▁Since ▁there ▁is ▁a ▁carry ▁in ▁column ▁ 5 , ▁O ▁must ▁be ▁less ▁than ▁or ▁equal ▁to ▁M ▁( from ▁column ▁ 4 ). ▁But ▁O ▁cannot ▁be ▁equal ▁to ▁M ,