Suppose a four digit code is created for each person in a gr…

Suppose a four digit code is created for each person in a group so that the fourth digit is assigned to make the sum of all four digits divisible by 7. The digits 0 through 9 may be used. What would then fourth digit have to be to make 836 a valid four digit identification number under this system?

A country has three provinces called Red, Blue, and Yellow,…

A country has three provinces called Red, Blue, and Yellow, and the country is apportioning seats in a legislature. The standard quotas for Red, Blue, and Yellow are 20.4, 12.24, and 18.36 respectively. Using Hamilton’s method, which province will be first to receive a leftover seat (if there are any left over?)