Fibonacci series?
A man takes a 10-day job. His boss tells him he'll be paid his boss's age on the first day and his boss's weight on the second day. The third day's wage will be the sum of the first two, the fourth day's wage the sum of the 2nd and 3rd, and each subsequent day's wage will be the sum of the previous two. The man is only told the total payment, for the boss doesn't want to reveal his age or weight.
The man asks his boss to see just one of the day's wage (after the 2nd), knowing that he can calculate the age and weight from knowing one day's wage and the total sum.
The boss, wanting to conceal his age and weight, agrees to show him which day's wage?
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1 solution
Let a 1 be his salary on Day 1 and a 2 be his salary on Day 2. Each succeeding day's salary can be expressed in terms of a 1 and a 2 . We note that his total salary is S t o t a l = 1 4 3 a 1 + 8 8 a 2 . His Day 7 salary is D 7 = 1 3 a 1 + 8 a 2 . He will not be able to solve a 1 and a 2 because the determinant of the coefficient matrix is 0 . This is not true for all the other days. *Notice that 1 1 ( 1 3 a 1 + 8 a 2 ) = 1 4 3 a 1 + 8 8 a 2 .