* 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 Sept 23 – Sept 29: **All to do with exponents. How many of the following can you do in your head?**

Click GoogleForm to submit answers by Sat, Sept 29.

Sept 23: Express as a power of 4.

Answer:

Sept 24: Express as a power of 2.

Answer:

Sept 25: Express as a power of .

Answer:

Sept 26: When the expression is multiplied out, how many digits does the number have?

Answer: has 25 digits

Sept 27: What is the sum of the digits of the number ?

Answer: . The sum of digits is 12.

Sept 28: What is the positive integer for which ?

Answer:

Sept 29: What is the value of such that ?

Answer: 18

Week of Sept 16 – Sept 22: **Can you do the following calculations in your head?**

Click GoogleForm to submit answers by Sat, Sept 29.

Sept 16: What is the product of ?

Answer:

Sept 17: What is the sum of the first 40 positive integers?

Answer:

Sept 18: What is the value of 123,123 divided by 1001?

Answer: 123

Sept 19: What is the sum (-100) + (-99) + (-98) + … + 97 + 98?

Answer: -199

Sept 20: What is sum (-39) + (-37) + (-35) + … (-3) + (-1)?

Answer:

Sept 21: What is the value of 100 – 99 + 98 – 97 + … + 4 – 3 + 2 – 1?

Answer: 50

Sept 22: If 222,222 is the product of 37,037 and 6, what is the product of 37,037 and 27?

Answer: 999999