Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 10
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1310. If John celebrated his 16
birthday on Wednesday, February 10 , 2016, what day of
the week was he born? (Don’t forget about leap years!)
Clearly John was born in the year 2000. Since his birthday is before February 29 , he
would have lived through 4 leap years (2000, 2004, 2008 and 2012) and 12 years with
365 days each. So we want to calculate:
[(365
12) + (366
4)] (mod 7) = [(1
5) + +(2
4)] (mod 7) = 5 + 8 (mod 7) = 6
This means that his 16 birthday fell 6 days (in the week) after the day on which he
was born.
So if we work backwards, 6 days before Wednesday is Thursday.
John was born on Thursday, February 10 , 2000.
11. Mary is facing South and rotates 2295° clockwise. Which direction is she facing now?
We want to know how many degrees she rotated CW from South. So we calculate:
2295 (mod 360) = 135
Mary rotated 135°clockwise and so she would be facing North-West.
N
W
E
S
12. (a) How many different 5-digit binary numbers are there?
Solution 1:
We will first approach this question by looking into how many possibilities there are
for each of the 5 digits.
1
1
1
1
1
0
0
0
0
1
2
2
2
2
=
16
Notice that the only possible number in the first digit is 1, if it were 0 it would be
considered a 4-digit binary number.
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