In the electronic clock display below all digits are different when, for example, hh=07, mm=20 and ss=15. How many times between 7:00:00 to 8:00:00 will all digits be different?

Select An Answer

A

1242

B

1248

C

1254

D

1260

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$. For h there is only one choice, namely 7. $m_1$ and $s_1$ each to be filled in with digits 0 to 5, 6 choices for $m_1$ and 5 choices for $s_1$ $($different from $m_1)$. $m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 7 and not the numbers used in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$. \begin{equation*} 1\times 6 \times 7 \times 5 \times 6 = 1260 \end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$. For h there is only one choice, namely 7. $m_1$ and $s_1$ each to be filled in with digits 0 to 5, 6 choices for $m_1$ and 5 choices for $s_1$ $($different from $m_1)$. $m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 7 and not the numbers used in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$. \begin{equation*} 1\times 6 \times 7 \times 5 \times 6 = 1260 \end{equation*}

In the electronic clock display below all digits are different when, for example,
$hh=00$, $mm=12$ and $ss=34$.
How many times between 0:00:00 to 1:00:00 will all digits be different?

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 0.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 0 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=01, mm=02 and ss=34.
How many times between 1:00:00 to 2:00:00 will all digits be different?

Select An Answer

A

840

B

850

C

860

D

870

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 1.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 1 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 1.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 1 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=02, mm=01 and ss=34.
How many times between 2:00:00 to 3:00:00 will all digits be different?

Select An Answer

A

840

B

850

C

860

D

870

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 2.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 2 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 2.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 2 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=03, mm=01 and ss=24.
How many times between 3:00:00 to 4:00:00 will all digits be different?

Select An Answer

A

840

B

850

C

860

D

870

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 3.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 3 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 3.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 3 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=04, mm=01 and ss=23.
How many times between 4:00:00 to 5:00:00 will all digits be different?

Select An Answer

A

820

B

830

C

840

D

850

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 4.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 4 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 4.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 4 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=05, mm=01 and ss=23.
How many times between 5:00:00 to 6:00:00 will all digits be different?

Select An Answer

A

810

B

820

C

830

D

840

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 5.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 5 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 5.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
5 choices for $m_1$ and 4 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 5 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 5 \times 7 \times 4 \times 6 = 840
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=06, mm=01 and ss=23.
How many times between 6:00:00 to 7:00:00 will all digits be different?

Select An Answer

A

1250

B

1260

C

1270

D

1280

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 6.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 6 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 6.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 6 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=07, mm=01 and ss=23.
How many times between 7:00:00 to 8:00:00 will all digits be different?

Select An Answer

A

1250

B

1260

C

1270

D

1280

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 7.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 7 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 7.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 7 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=08, mm=01 and ss=23.
How many times between 8:00:00 to 9:00:00 will all digits be different?

Select An Answer

A

1260

B

1270

C

1280

D

1290

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 8.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 8 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 8.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 8 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

In the electronic clock display below all digits are different when, for example,
hh=09, mm=01 and ss=23.
How many times between 9:00:00 to 10:00:00 will all digits be different?

Select An Answer

A

1250

B

1260

C

1270

D

1280

Sorry. Please check the correct answer below.

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 9.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 9 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}

Let the format of digital clock be $h:m_1m_2:s_1s_2$.
For h there is only one choice, namely 9.
$m_1$ and $s_1$ each to be filled in with digits 0 to 5,
6 choices for $m_1$ and 5 choices for $s_1$ (different from $m_1$).
$m_2$ and $s_2$ each to be filled in with digits 0 to 9, but not 9 and not the numbers used
in $m_1$ and $s_1$, so 7 choices for $m_2$ and 6 choices for $s_2$ $($different from $m_2)$.
\begin{equation*}
1 \times 6 \times 7 \times 5 \times 6 = 1260
\end{equation*}