There is a machine A which displays the number of 2 digits and when a switch is turned on, numbers will be displayed according to the following rule for every second.
<Rule 1>
<Rule 1>
Tens digit changes for every second in order of 1, 2, 3, 4, 5, 6, 7, and 8, and after 8 returns to 1 again and changes in the same rule.
<Rule 2>
<Rule 2>
Ones digit changes for every second in order of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, and after 0 returns to 1 again and changes in the same rule.
For example, when a switch is turned on, 11 will be displayed one second after, 22 will be two seconds after, 33 will be three seconds after and 19 will be nine seconds after, 20 will be ten seconds after and 31 will be 11 seconds after.
Answer the following questions.
(1) Find the number of seconds when 73 is displayed first after the switch is turning on.
(2) Find the sum total which added all of the number of two digits which can be displayed by this machine A.
(3) There is a machine B which displays the number of three digits like machine A.
The rule displaying tens digit and ones digit is the same as the machine A.
As for hundreds digit, it changes for every second in order of 7, 6, 5, 4, 3, 2, and 1 and after 1 returns to 7 again and changes in the same rule.
For example, when a switch is turned on, 711 will be displayed one second after, 622 will be two seconds after and 788 will be eight seconds after.
(3)-1 Find the time when 711 is displayed 2nd time after the switch was turned on.
(3)-2 Find the time when 773 is displayed first time after the switch was turned on.
Answer
(1) 23 seconds
(2) 1980
(3)-1 281 seconds
(3)-2 183 seconds
(2) 1980
(3)-1 281 seconds
(3)-2 183 seconds
