House Apportionment worksheet

1. Seats per state: Northmere 10, Eastbrook 1, Lakeland 3, Southvale 3, Westridge 2, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 14 of the 20 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 16 goes to Southvale, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{1,790,693}}{\sqrt{2\times 3}}$$=\mathrm{731,047.36}$

4. Seat 17 goes to Northmere, its 8th. With 7 seats, its priority value is the highest left.

   $\frac{\mathrm{5,286,610}}{\sqrt{7\times 8}}$$=\mathrm{706,452.98}$

5. Seat 18 goes to Lakeland, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{1,692,916}}{\sqrt{2\times 3}}$$=\mathrm{691,130.06}$

6. Seat 19 goes to Northmere, its 9th. With 8 seats, its priority value is the highest left.

   $\frac{\mathrm{5,286,610}}{\sqrt{8\times 9}}$$=\mathrm{623,032.96}$

7. Seat 20 goes to Northmere, its 10th. With 9 seats, its priority value is the highest left.

   $\frac{\mathrm{5,286,610}}{\sqrt{9\times 10}}$$=\mathrm{557,257.62}$

8. Next in line: if the House had 21 seats, the extra seat would go to Westridge, whose priority value is now the highest.

   $\frac{\mathrm{1,268,789}}{\sqrt{2\times 3}}$$=\mathrm{517,980.94}$

9. The final seats per state.

   $\text{Northmere 10, Eastbrook 1, Lakeland 3, Southvale 3, Westridge 2, Highfield 1}$

2. Seats per state: Northmere 3, Eastbrook 5, Lakeland 1, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 6 of the 12 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 8 goes to Northmere, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{3,589,724}}{\sqrt{1\times 2}}$$=\mathrm{2,538,318.18}$

4. Seat 9 goes to Eastbrook, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{5,943,968}}{\sqrt{2\times 3}}$$=\mathrm{2,426,614.77}$

5. Seat 10 goes to Eastbrook, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{5,943,968}}{\sqrt{3\times 4}}$$=\mathrm{1,715,875.76}$

6. Seat 11 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{3,589,724}}{\sqrt{2\times 3}}$$=\mathrm{1,465,498.69}$

7. Seat 12 goes to Eastbrook, its 5th. With 4 seats, its priority value is the highest left.

   $\frac{\mathrm{5,943,968}}{\sqrt{4\times 5}}$$=\mathrm{1,329,111.65}$

8. Next in line: if the House had 13 seats, the extra seat would go to Eastbrook, whose priority value is now the highest.

   $\frac{\mathrm{5,943,968}}{\sqrt{5\times 6}}$$=\mathrm{1,085,215.12}$

9. The final seats per state.

   $\text{Northmere 3, Eastbrook 5, Lakeland 1, Southvale 1, Westridge 1, Highfield 1}$

3. Seats per state: Northmere 4, Eastbrook 1, Lakeland 1, Southvale 2, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 4 of the 10 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 7 goes to Northmere, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{4,123,777}}{\sqrt{1\times 2}}$$=\mathrm{2,915,950.68}$

4. Seat 8 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{4,123,777}}{\sqrt{2\times 3}}$$=\mathrm{1,683,524.91}$

5. Seat 9 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{4,123,777}}{\sqrt{3\times 4}}$$=\mathrm{1,190,431.88}$

6. Seat 10 goes to Southvale, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{1,400,187}}{\sqrt{1\times 2}}$$=\mathrm{990,081.72}$

7. Next in line: if the House had 11 seats, the extra seat would go to Northmere, whose priority value is now the highest.

   $\frac{\mathrm{4,123,777}}{\sqrt{4\times 5}}$$=\mathrm{922,104.57}$

8. The final seats per state.

   $\text{Northmere 4, Eastbrook 1, Lakeland 1, Southvale 2, Westridge 1, Highfield 1}$

4. Seats per state: Northmere 8, Eastbrook 7, Lakeland 2, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 14 of the 20 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 16 goes to Eastbrook, its 6th. With 5 seats, its priority value is the highest left.

   $\frac{\mathrm{4,772,059}}{\sqrt{5\times 6}}$$=\mathrm{871,254.79}$

4. Seat 17 goes to Northmere, its 7th. With 6 seats, its priority value is the highest left.

   $\frac{\mathrm{4,977,279}}{\sqrt{6\times 7}}$$=\mathrm{768,010.82}$

5. Seat 18 goes to Eastbrook, its 7th. With 6 seats, its priority value is the highest left.

   $\frac{\mathrm{4,772,059}}{\sqrt{6\times 7}}$$=\mathrm{736,344.69}$

6. Seat 19 goes to Lakeland, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{946,427}}{\sqrt{1\times 2}}$$=\mathrm{669,224.95}$

7. Seat 20 goes to Northmere, its 8th. With 7 seats, its priority value is the highest left.

   $\frac{\mathrm{4,977,279}}{\sqrt{7\times 8}}$$=\mathrm{665,116.88}$

8. Next in line: if the House had 21 seats, the extra seat would go to Eastbrook, whose priority value is now the highest.

   $\frac{\mathrm{4,772,059}}{\sqrt{7\times 8}}$$=\mathrm{637,693.21}$

9. The final seats per state.

   $\text{Northmere 8, Eastbrook 7, Lakeland 2, Southvale 1, Westridge 1, Highfield 1}$

5. Seats per state: Northmere 4, Eastbrook 2, Lakeland 1, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 4 of the 10 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 7 goes to Northmere, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{6,078,022}}{\sqrt{1\times 2}}$$=\mathrm{4,297,810.57}$

4. Seat 8 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{6,078,022}}{\sqrt{2\times 3}}$$=\mathrm{2,481,342.09}$

5. Seat 9 goes to Eastbrook, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{2,713,418}}{\sqrt{1\times 2}}$$=\mathrm{1,918,676.27}$

6. Seat 10 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{6,078,022}}{\sqrt{3\times 4}}$$=\mathrm{1,754,573.82}$

7. Next in line: if the House had 11 seats, the extra seat would go to Lakeland, whose priority value is now the highest.

   $\frac{\mathrm{2,472,752}}{\sqrt{1\times 2}}$$=\mathrm{1,748,499.71}$

8. The final seats per state.

   $\text{Northmere 4, Eastbrook 2, Lakeland 1, Southvale 1, Westridge 1, Highfield 1}$

6. Seats per state: Northmere 5, Eastbrook 2, Lakeland 1, Southvale 2, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 6 of the 12 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 8 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{3,483,499}}{\sqrt{2\times 3}}$$=\mathrm{1,422,132.51}$

4. Seat 9 goes to Eastbrook, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{1,489,021}}{\sqrt{1\times 2}}$$=\mathrm{1,052,896.85}$

5. Seat 10 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{3,483,499}}{\sqrt{3\times 4}}$$=\mathrm{1,005,599.54}$

6. Seat 11 goes to Southvale, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{1,325,345}}{\sqrt{1\times 2}}$$=\mathrm{937,160.44}$

7. Seat 12 goes to Northmere, its 5th. With 4 seats, its priority value is the highest left.

   $\frac{\mathrm{3,483,499}}{\sqrt{4\times 5}}$$=\mathrm{778,934.06}$

8. Next in line: if the House had 13 seats, the extra seat would go to Northmere, whose priority value is now the highest.

   $\frac{\mathrm{3,483,499}}{\sqrt{5\times 6}}$$=\mathrm{635,996.99}$

9. The final seats per state.

   $\text{Northmere 5, Eastbrook 2, Lakeland 1, Southvale 2, Westridge 1, Highfield 1}$

7. Seats per state: Northmere 4, Eastbrook 4, Lakeland 1, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 6 of the 12 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 8 goes to Eastbrook, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{5,172,902}}{\sqrt{1\times 2}}$$=\mathrm{3,657,794.08}$

4. Seat 9 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{5,245,689}}{\sqrt{2\times 3}}$$=\mathrm{2,141,543.57}$

5. Seat 10 goes to Eastbrook, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{5,172,902}}{\sqrt{2\times 3}}$$=\mathrm{2,111,828.4}$

6. Seat 11 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{5,245,689}}{\sqrt{3\times 4}}$$=\mathrm{1,514,299.98}$

7. Seat 12 goes to Eastbrook, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{5,172,902}}{\sqrt{3\times 4}}$$=\mathrm{1,493,288.18}$

8. Next in line: if the House had 13 seats, the extra seat would go to Southvale, whose priority value is now the highest.

   $\frac{\mathrm{1,805,891}}{\sqrt{1\times 2}}$$=\mathrm{1,276,957.77}$

9. The final seats per state.

   $\text{Northmere 4, Eastbrook 4, Lakeland 1, Southvale 1, Westridge 1, Highfield 1}$

8. Seats per state: Northmere 4, Eastbrook 2, Lakeland 1, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 4 of the 10 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 7 goes to Northmere, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{8,031,255}}{\sqrt{1\times 2}}$$=\mathrm{5,678,954.87}$

4. Seat 8 goes to Eastbrook, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{5,516,812}}{\sqrt{1\times 2}}$$=\mathrm{3,900,975.18}$

5. Seat 9 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{8,031,255}}{\sqrt{2\times 3}}$$=\mathrm{3,278,746.12}$

6. Seat 10 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{8,031,255}}{\sqrt{3\times 4}}$$=\mathrm{2,318,423.62}$

7. Next in line: if the House had 11 seats, the extra seat would go to Eastbrook, whose priority value is now the highest.

   $\frac{\mathrm{5,516,812}}{\sqrt{2\times 3}}$$=\mathrm{2,252,229.07}$

8. The final seats per state.

   $\text{Northmere 4, Eastbrook 2, Lakeland 1, Southvale 1, Westridge 1, Highfield 1}$

9. Seats per state: Northmere 4, Eastbrook 1, Lakeland 2, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 4 of the 10 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 7 goes to Northmere, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{7,323,546}}{\sqrt{1\times 2}}$$=\mathrm{5,178,529.04}$

4. Seat 8 goes to Northmere, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{7,323,546}}{\sqrt{2\times 3}}$$=\mathrm{2,989,825.13}$

5. Seat 9 goes to Northmere, its 4th. With 3 seats, its priority value is the highest left.

   $\frac{\mathrm{7,323,546}}{\sqrt{3\times 4}}$$=\mathrm{2,114,125.63}$

6. Seat 10 goes to Lakeland, its 2nd. With 1 seat, its priority value is the highest left.

   $\frac{\mathrm{2,828,420}}{\sqrt{1\times 2}}$$=\mathrm{1,999,994.96}$

7. Next in line: if the House had 11 seats, the extra seat would go to Northmere, whose priority value is now the highest.

   $\frac{\mathrm{7,323,546}}{\sqrt{4\times 5}}$$=\mathrm{1,637,594.67}$

8. The final seats per state.

   $\text{Northmere 4, Eastbrook 1, Lakeland 2, Southvale 1, Westridge 1, Highfield 1}$

10. Seats per state: Northmere 8, Eastbrook 1, Lakeland 3, Southvale 1, Westridge 1, Highfield 1

1. Give each of the 6 states its minimum of 1 seat. That leaves 9 of the 15 seats to give out by priority.

   $6\times 1$$=6$

2. Give out the other seats one at a time, each to the state with the highest priority value. That value is the population (P) divided by the square root of n(n + 1), where n is the seats it has so far.

   $\mathrm{priority}$$=\frac{P}{\sqrt{n\times \left(n+1\right)}}$

3. Seat 11 goes to Northmere, its 5th. With 4 seats, its priority value is the highest left.

   $\frac{\mathrm{7,999,638}}{\sqrt{4\times 5}}$$=\mathrm{1,788,773.44}$

4. Seat 12 goes to Northmere, its 6th. With 5 seats, its priority value is the highest left.

   $\frac{\mathrm{7,999,638}}{\sqrt{5\times 6}}$$=\mathrm{1,460,527.39}$

5. Seat 13 goes to Lakeland, its 3rd. With 2 seats, its priority value is the highest left.

   $\frac{\mathrm{3,138,652}}{\sqrt{2\times 3}}$$=\mathrm{1,281,349.31}$

6. Seat 14 goes to Northmere, its 7th. With 6 seats, its priority value is the highest left.

   $\frac{\mathrm{7,999,638}}{\sqrt{6\times 7}}$$=\mathrm{1,234,370.94}$

7. Seat 15 goes to Northmere, its 8th. With 7 seats, its priority value is the highest left.

   $\frac{\mathrm{7,999,638}}{\sqrt{7\times 8}}$$=\mathrm{1,068,996.59}$

8. Next in line: if the House had 16 seats, the extra seat would go to Northmere, whose priority value is now the highest.

   $\frac{\mathrm{7,999,638}}{\sqrt{8\times 9}}$$=\mathrm{942,766.38}$

9. The final seats per state.

   $\text{Northmere 8, Eastbrook 1, Lakeland 3, Southvale 1, Westridge 1, Highfield 1}$