Question 40
A Mystic Four Calculator has a four-digit display and four buttons. The calculator works as follows: Pressing button 1 replaces the number in the display with $1$; Pressing button 2 divides the number in the display by $2$; Pressing button 3 subtracts $3$ from the number in the display; Pressing button 4 multiplies the number in the display by $4$.
Initially the display shows $0$. Any operation yielding a negative, fractional, or five-digit answer is ignored.
a. Can $2007$ appear in the display?
b. Can $2008$ appear in the display?
Initially the display shows $0$. Any operation yielding a negative, fractional, or five-digit answer is ignored.
a. Can $2007$ appear in the display?
b. Can $2008$ appear in the display?