Question

Suppose Haruka has a special key $\Delta$ in her calculator called delta key:

Rule 1: If the display shows a one-digit number, pressing delta key $\Delta$ replaces the displayed number with twice its value. Rule 2: If the display shows a two-digits number, pressing delta key $\Delta$ replaces the displayed number with the number sum of two digits.

Suppose Haruka enters the value 1 and then presses delta key $\Delta$ repeatedly. After pressing the key for 68 times, what will be the displayed number?

Accepted Answer

A. Starting at 1: Press 1: $1 	imes 2 = 2$ Press 2: $2 	imes 2 = 4$ Press 3: $4 	imes 2 = 8$ Press 4: $8 	imes 2 = 16$ Press 5: $1 + 6 = 7$ Press 6: $7 	imes 2 = 14$ Press 7: $1 + 4 = 5$ Press 8: $5 	imes 2 = 10$ Press 9: $1 + 0 = 1$ The cycle repeats every 9 presses. $68 = 9 	imes 7 + 5$. So after 68 presses, the result corresponds to the 5th press, which is 7.

Delta Key Calculator Pattern

Explanation

Practise this under exam conditions