The equity sections for Atticus Group at the beginning of the year $($January $1)$ and end of the year $($December $31)$ follow.

Stockholders$$ Equity $($January $1)$

Common stock$$$$6$ par value, $100,000$ shares authorized, $30,000$ shares issued and outstanding $ $180,000$

Paid$-$in capital in excess of par value, common stock $140,000$

Retained earnings $340,000$

Total stockholders$$ equity $ $660,000$

Stockholders$$ Equity $($December $31)$

Common stock$$$$6$ par value, $100,000$ shares authorized, $35,400$ shares issued, $3,000$ shares in treasury $ $212,400$

Paid$-$in capital in excess of par value, common stock $172,400$

Retained earnings $($$$40,000$ restricted by treasury stock$)440,000$

$824,800$

Less cost of treasury stock $(40,000)$

Total stockholders$$ equity $ $784,800$

The following transactions and events affected its equity during the year.

January $5$ Declared a $$0\mathrm{.}50$ per share cash dividend, date of record January $10.$

March $20$ Purchased treasury stock for cash.

April $5$ Declared a $$0\mathrm{.}50$ per share cash dividend, date of record April $10.$

July $5$ Declared a $$0\mathrm{.}50$ per share cash dividend, date of record July $10.$

July $31$ Declared a $20\%$ stock dividend when the stock$$s market value was $$12$ per share.

August $14$ Issued the stock dividend that was declared on July $31.$

October $5$ Declared a $$0\mathrm{.}50$ per share cash dividend, date of record October $10.$

Required:

$1.$ How many common shares are outstanding on each cash dividend date?