MathCastle
Groups and FieldsEasyGroups and the Group Axioms

Groups and the Group Axioms · Easy problem

A dial lock works in the group (Z10,+)(\mathbb Z_{10},+): turning it by aa clicks then by bb clicks is the same as turning it by a+ba+b clicks mod 1010, and position 00 means "unlocked". The dial has just been turned by 66 clicks. How many more clicks xx (with 0≤x<100\le x<10) are needed to return it to position 00?