* I will post* seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

* For instructions* on submitting weekly answers, click on the “Logistics” tab.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*Week of Oct 14 – Oct 20: **Inequalities. **

Click GoogleForm to submit answers by Sat, Oct 20.

**Determine whether each of the statements is true or false. If false, provide an example that shows the statement is false.**

Oct 14: If and , then .

Oct 15: If , then .

Oct 16: If , then .

Oct 17: If , then .

Oct 18: If and , then .

Oct 19: If , then .

Oct 20: If , then .

Week of Oct 7 – Oct 13: **Equations.**

Click GoogleForm to submit answers by Sat, Oct 13.

Oct 7: If , what is ?

Answer: , , .

Oct 8: Solve for : .

Answer: 11111

Oct 9: Solve for :

Answer: 11/5

Oct 10: For what number , does the equation have infinitely many solutions for ?

Answer:

Oct 11: For what numbers , does the equation have no solutions for ?

Answer:

Oct 12: For what value of , can we not determine the value of ?

Answer:

Oct 13: A number is twice its reciprocal. What is ?

Answer: . Therefore,

Week of Sept 30 – Oct 6: **All to do with factors.**

Click GoogleForm to submit answers by Sat, Oct 6.

Sept 30: Without doing the actual division, can you tell which of the following numbers is *not* divisible by 4?

2884, 201846, 9164, 7632, 79828

Answer: 201846

Oct 1: Without doing the actual division, can you tell which of the following numbers is *not* divisible by 8?

7248, 2018640, 100036, 1032, 88056

Answer: 100036

Oct 2: Without doing the actual division, can you tell which of the following numbers is divisible by 9?

4562, 56233, 12345678, 60231, 9671001

Answer: 12345678

Oct 3: What is the smallest prime factor of ?

Answer: 2

Oct 4: If 18 is a factor of , what other positive numbers must be factors of ?

Answer: 1, 2, 3, 6, 9

Oct 5: What is the units digit of the product of any five consecutive positive integers?

Answer: 0

Oct 6: If the four-digit number is divisible by 6, what is the largest possible value of the digit ?

Answer: 7