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Difference between revisions of "Mathtime Version 1 Edition 1"

m (moved Mathtime Edition 1 to Mathtime Version 1 Edition 1: Need more specific title.)
 
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== Number Theory ==
 
== Number Theory ==
  
−
=Problem 1=
+
===Problem 1===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447930 <math>\boxed{1}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447930 <math>\boxed{1}</math>]
  
 
What is the last digit of the product of all odd integers between <math>1</math> and <math>1,000?</math>
 
What is the last digit of the product of all odd integers between <math>1</math> and <math>1,000?</math>
  
−
=Problem 2=
+
===Problem 2===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447931 <math>\boxed{2}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447931 <math>\boxed{2}</math>]
  
Line 16: Line 16:
 
(Inspiration of Problem: Alcumus/AMC 8)
 
(Inspiration of Problem: Alcumus/AMC 8)
  
−
=Problem 3=
+
===Problem 3===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447932 <math>\boxed{3}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447932 <math>\boxed{3}</math>]
  
 
What is <math>\dfrac{4042110}{4038090}?</math>
 
What is <math>\dfrac{4042110}{4038090}?</math>
  
−
=Problem 4=
+
===Problem 4===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447935 <math>\boxed{4}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447935 <math>\boxed{4}</math>]
  
 
What is the sum of the digits of the square root of <math>9801?</math>
 
What is the sum of the digits of the square root of <math>9801?</math>
  
−
=Problem 5=
+
===Problem 5===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447936 <math>\boxed{5}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447936 <math>\boxed{5}</math>]
  
 
Find the sum of the digits of <math>35435_{7}+13362_{7}</math> in base <math>7</math>.
 
Find the sum of the digits of <math>35435_{7}+13362_{7}</math> in base <math>7</math>.
  
−
=Problem 6=
+
===Problem 6===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447937 <math>\boxed{6}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447937 <math>\boxed{6}</math>]
  
 
Find <math>111_{2}+222_{4}+444_{8}</math> in binary form.
 
Find <math>111_{2}+222_{4}+444_{8}</math> in binary form.
  
−
=Problem 7=
+
===Problem 7===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447938 <math>\boxed{7}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447938 <math>\boxed{7}</math>]
  
 
Find the difference between <math>444_{8}</math> and <math>222_{4}</math> in base 8.
 
Find the difference between <math>444_{8}</math> and <math>222_{4}</math> in base 8.
  
−
=Problem 8=
+
===Problem 8===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447939 <math>\boxed{8}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447939 <math>\boxed{8}</math>]
  
 
In what base is <math>66+87+85+48</math> equal to <math>132?</math>
 
In what base is <math>66+87+85+48</math> equal to <math>132?</math>
  
−
=Problem 9=
+
===Problem 9===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447940 <math>\boxed{9}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447940 <math>\boxed{9}</math>]
  
 
Find the value of <math>324_{5}+18_{10}</math> in base ten.
 
Find the value of <math>324_{5}+18_{10}</math> in base ten.
  
−
=Problem 10=
+
===Problem 10===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447941 <math>\boxed{10}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447941 <math>\boxed{10}</math>]
  
 
What is <math>0_{4}</math>, <math>1_{4}</math>, <math>2_{4}</math>, <math>3_{4}</math>, and <math>1230_{4}</math> in binary form?
 
What is <math>0_{4}</math>, <math>1_{4}</math>, <math>2_{4}</math>, <math>3_{4}</math>, and <math>1230_{4}</math> in binary form?
  
−
=Problem 11=
+
===Problem 11===
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447942 <math>\boxed{11}</math>]
 
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=768&t=447942 <math>\boxed{11}</math>]
  
 
<math>n\equiv0\pmod{3}</math>, <math>n\equiv0\pmod{7}</math>, and <math>n\equiv1\pmod{8}</math>. What is the smallest positive integer that satisfies the above?
 
<math>n\equiv0\pmod{3}</math>, <math>n\equiv0\pmod{7}</math>, and <math>n\equiv1\pmod{8}</math>. What is the smallest positive integer that satisfies the above?

Latest revision as of 11:29, 2 December 2011

Mathtime Magazine Volume 1 Edition 1 is here


Number Theory

Problem 1

$\boxed{1}$

What is the last digit of the product of all odd integers between $1$ and $1,000?$

Problem 2

$\boxed{2}$

What is the $2011$th letter in the sequence $\text{MATHLETEMATHLETEMATHLETE}\ldots?$

(Inspiration of Problem: Alcumus/AMC 8)

Problem 3

$\boxed{3}$

What is $\dfrac{4042110}{4038090}?$

Problem 4

$\boxed{4}$

What is the sum of the digits of the square root of $9801?$

Problem 5

$\boxed{5}$

Find the sum of the digits of $35435_{7}+13362_{7}$ in base $7$.

Problem 6

$\boxed{6}$

Find $111_{2}+222_{4}+444_{8}$ in binary form.

Problem 7

$\boxed{7}$

Find the difference between $444_{8}$ and $222_{4}$ in base 8.

Problem 8

$\boxed{8}$

In what base is $66+87+85+48$ equal to $132?$

Problem 9

$\boxed{9}$

Find the value of $324_{5}+18_{10}$ in base ten.

Problem 10

$\boxed{10}$

What is $0_{4}$, $1_{4}$, $2_{4}$, $3_{4}$, and $1230_{4}$ in binary form?

Problem 11

$\boxed{11}$

$n\equiv0\pmod{3}$, $n\equiv0\pmod{7}$, and $n\equiv1\pmod{8}$. What is the smallest positive integer that satisfies the above?

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