Quandaries
and Queries 

My daughter has a math problem involving exponential equations which we are wondering about. "Juan wrote the first 12 powers of 2. He noticed a pattern in the digits in the units places of the results. He said he could use this pattern to predict the digits for 2 to the power of 100. " What is the "digit in the units place?" 

Hi Gerald, Did you write the first 12 powers of 2? Try the first few cases and look at the units digit only (you don't have to do the powers of 2 just the last digit remember).
When you multiply by 2 repeatedly you'll notice the cyclic behavior of this last digit  so for example 2^{20} will have a 6 as its last digit. How about 2^{35}, 2^{57}, ..., 2^{100}? Penny 

