







The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





Units digit 
20140103 

From gracie: 9^23 units digit Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





The units digit 
20120911 

From Shaunice: Simplify each of the following expressions and determine what the last
digit would be.
a. (24^15) 4 Answered by Penny Nom. 





A snail on an elastic band 
20100203 

From Joe: A snail starts crawling from one end along a uniformly stretched elastic band. It crawls at a rate of 1 foot per minute. The band is initially 10 feet long and is instantaneously and uniformly stretched an additional 10 feet at the end of each minute. The snail maintains his grip on the band during the instant of each stretch. At what points in time is the snail
(a) closest to the far end of the band, and
(b) farthest from the far end of the band? Answered by Robert Dawson. 





Units digit 
20090723 

From Jyll: How do solve for the units digit? And that, what is the units digit of the first 1000 prime numbers? Answered by Robert Dawson. 





The diameter of a roll of plastic 
20090324 

From truong: hi. i have trouble to calculate the diameter of the plastic roll. the sheet is 765 m long and 0.8 mm to wrap around the core 400 mm in dia. please help me with the formula to calculate the dia of plastic roll, thanks in advance Answered by Harley Weston. 





The units digit of 2^95 
20090318 

From Sharvon: what is the units digit of 2^95 Answered by Robert Dawson. 





The 2 rightmost digits 
20081218 

From Peter: Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993? Answered by Robert Dawson and Victoria West. 





The last two digits 
20060722 

From Sam: You have answered this question already but you only answered to one digit.
What are the last TWO digits of:
3 to the power of 1994
7 to the power of 1994
3 to the power of 1994 + 7 to the power of 1994
7 to the power of 1994  3 to the power of 1994
Answered by Paul Betts and Penny Nom. 





n^2+n1 has no divisors ending with 3 or 7 
20050908 

From Arne: at least it seems like for any integers n and k,
10k+3 and 10k+7 do not divide nē+n1
I tested this for every n from 0 to 3200 (which means same for the numbers from 3201 to 1)
could this be true, or is it just coincidence, or am I just totally wrong? Answered by Richard McIntosh. 





The last digit of a large exponent 
20041020 

From Landon: How can one determine the last digit of a large exponent by hand. I have seen several examples of how to do this by breaking it up into smaller exponents, but is there a formula or some common things to look for? Answered by Penny Nom. 





The last digit of 2^28 
20040925 

From A student: I am currently enrolled in a math reasoning class and a math question I have to answer is determine the units digit in 3 28power. When I set up a table and keep cubing the numbers, I find a pattern with the last digits of the numbers that follow 1,3,9,7. My calculator gets to about the 19th power, and then I get an error. If I continued the pattern, would the units digit then be the last digit of 3 28th power, which would be a 7? Please let me know if I am solving this correctly and what a unit's digit actually is. Answered by Penny Nom. 





The units digit of 57 to the 28th power 
20030901 

From Maria:
If 57 is raised to the 28th power, what must be the units digit in the result? If you raise 7 to the 500th power, what is the numeral that will appear in the units digit position? Answered by Penny Nom. 

