self Maths Puzzle


Firoz has a certain amount of money in only Re 1 and Rs 10 notes. The number of Re 1 notes multiplied by the number of Rs 10 notes is equal to the total money (in Rs) that he has. The number of Rs 10 notes is less than ten. Which of the following is a possible figure for the total number of notes he can have?

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PQRSTU is a regular hexagon drawn on the ground. Prashant stands at P and he starts jumping from vertex to vertex beginning from P. From any vertex of the hexagon except S, which is opposite to A, he may jump to any adjacent vertices. When he reaches S, he stops. Let Sn be the number of distinct paths of exactly n jumps ending at S. What is the value of S2k, where k is an integer?

A lock has a code consisting of five distinct letters, from among the first eleven words of English alphabet. The lock opens, if any three letters of the code match occurring not in the same position. What is the least number of five-letter codes, one should try to be sure that the lock is opened