







Calendar arithmetic 
20160214 

Jenalee pose la question : January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC).
If Julian Day 0 was a Monday, what day of the week was January 1, 2001? Victoria West lui répond. 





Mod versus Rem in Turing 
20130101 

Eric pose la question : I am a teacher teaching computer science using Turing. I am having
difficulty understanding why one would use the mod operator versus the rem
remainder operator.
Mod seems to make the resulting sign depend on the sign of the divisor,
whereas rem makes the resulting sign depend on the dividend.
Examples:
11 mod 5 = 1 and 11 rem 5 =1
11 mod 5 = 4 and 11 rem 5 = 1
11 mod 5 = 4 and 11 rem 5 =1
11 mod 5 = 1 and 11 rem 5 = 1
What I can't understand is why this would matter. For example, 11 / 5 =
2.2 and 11 / 5 = 2.2 get the same result.
So how is a remainder dependent on the sign of one of the parts?
What benefit would using one over the other have?
Any insight would be most helpful!
Eric Harley Weston lui répond. 





Modular arithmetic 
20111030 

Kim pose la question : Hello,
I am editing a resource for students, and I think some of the answers may be incorrect.
The text I was given and my questions are in the attachment.
Any help you could give would be appreciated.
Thanks,
Kim Harley Weston lui répond. 





(x^3 + 11x) is divisible by 6 
20100624 

PT pose la question : Given that x is a nonzero integer,
how do you show that for all values of x,
(x3 + 11x) is divisible by 6?
I know it works but how do I answer the "all values of x" part?
Thanks in advance! Robert Dawson lui répond. 





Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: 
20050718 

Ladis pose la question : Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6. Chris Fisher lui répond. 





Take It! 
20020403 

Bryan pose la question : You are playing Take It! for $180,00 with a total stranger. There are 180 identical balls in a big vase. Each player in his turn, reaches into the vase and pulls out 1,5,or8 balls. These balls are discarded. The player who takes the last ball from the vase wins the $180,000. A flip of the coin determines that you will go first. Are you glad? How many will you take out on the first move, and how will you proceed to win the prize? Claude Tardif lui répond. 





Finding a formula 
20000505 

Erica Hildebrandt pose la question : If a farmer has a field and his plots are laid out in the following grid where each # represents a plot: 4  5  12  13  20  3  6  11  14  19  2  7  10  15  18  1  8  9  16  17  Of course the plot numbers aren't meaningful as I have described above. In fact they may not be numbers at all. The only constants I have are the total number of rows and columns. Using the total number of rows and columns and my current position row and column, how can I write a formula that tells me column 3 row 3 = 10, column 4 row 2 = 14, etc. I can see the pattern but can't quite get the formula. I believe I will need 2 different formulas one for even and one for odd rows. Paul Betts and Penny Nom lui répond. 





Divisibility by 9 
19990221 

Razzi pose la question : I've been having a hard time trying to solve the following problem and I was wondering if you could help me. For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b). Chris Fisher and Harley Weston lui répond. 





Modular Arithmetic 
19990204 

Leslie Kupper pose la question : I am trying to do a project on modular arithmetic. I was wondering if there were any websites that include a sample lesson plan on modular arithmetic for any grade level. Let me know where and how to find them. Thanks. Harley Weston lui répond. 





Clock Arithmetic. 
19980309 

Joann Dixon pose la question : What is clock mathematics? Patrick Maidorn lui répond. 

