Difference between revisions of "2013 PMWC"

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== Problem I1 ==
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The following is a list of [[PMWC]] problems from the year 2013
  
[[2013 PMWC Problems/Problem I1|Solution]]
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*[[2013 PMWC Problems|Entire Exam]]
 
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*[[2013 PMWC Answer Key|Answer Key]]
Nine cards are numbered from 1 to 9 respectively. Two cards are distributed to each of four children. The sum of the numbers on the two cards the children are given is: 7 for Ann, 10 for Ben, 11 for Cathy and 12 for Don. What is the number on the card that was not distributed?
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**[[2013 PMWC Problems/Problem I1|Problem I1]]
 
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**[[2013 PMWC Problems/Problem I2|Problem I2]]
== Problem I2 ==
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**[[2013 PMWC Problems/Problem I3|Problem I3]]
 
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**[[2013 PMWC Problems/Problem I4|Problem I4]]
[[2013 PMWC Problems/Problem I2|Solution]]
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**[[2013 PMWC Problems/Problem I5|Problem I5]]
 
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**[[2013 PMWC Problems/Problem I6|Problem I6]]
Given that ''A'', ''B'', ''C'' and ''D'' are distinct digits and
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**[[2013 PMWC Problems/Problem I7|Problem I7]]
 
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**[[2013 PMWC Problems/Problem I8|Problem I8]]
A A B C D - D A A B C = 2 0 1 3 D
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**[[2013 PMWC Problems/Problem I9|Problem I9]]
 
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**[[2013 PMWC Problems/Problem I10|Problem I10]]
Find A + B + C + D.
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**[[2013 PMWC Problems/Problem I11|Problem I11]]
 
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**[[2013 PMWC Problems/Problem I12|Problem I12]]
== Problem I3 ==
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**[[2013 PMWC Problems/Problem I13|Problem I13]]
 
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**[[2013 PMWC Problems/Problem I14|Problem I14]]
[[2013 PMWC Problems/Problem I3|Solution]]
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**[[2013 PMWC Problems/Problem I15|Problem I15]]
 
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**[[2013 PMWC Problems/Problem T1|Problem T1]]
A car traveled from Town A from Town B at an average speed of 100 km/h. It then traveled from Town B to Town C at an average speed of 75 km/h. Given that the distance from Town A to Town B is twice the distance from Town B to Town C, find the car's average speed, in km/h, for the entire journey.
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**[[2013 PMWC Problems/Problem T2|Problem T2]]
 
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**[[2013 PMWC Problems/Problem T3|Problem T3]]
== Problem I4 ==
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**[[2013 PMWC Problems/Problem T4|Problem T4]]
 
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**[[2013 PMWC Problems/Problem T5|Problem T5]]
[[2013 PMWC Problems/Problem I4|Solution]]
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**[[2013 PMWC Problems/Problem T6|Problem T6]]
 
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**[[2013 PMWC Problems/Problem T7|Problem T7]]
== Problem I5 ==
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**[[2013 PMWC Problems/Problem T8|Problem T8]]
 
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**[[2013 PMWC Problems/Problem T9|Problem T9]]
[[2013 PMWC Problems/Problem I5|Solution]]
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**[[2013 PMWC Problems/Problem T10|Problem T10]]
 
 
Find the sum of all the digits in the integers from 1 to 2013.
 
 
 
== Problem I6 ==
 
 
 
[[2013 PMWC Problems/Problem I6|Solution]]
 
 
 
What is the 2013th term in the sequence
 
 
 
<math>\frac{1}{1}</math> , <math>\frac{2}{1}</math> , <math>\frac{1}{2}</math> , <math>\frac{3}{1}</math> , <math>\frac{2}{2}</math> , <math>\frac{1}{3}</math> , <math>\frac{4}{1}</math> , <math>\frac{3}{2}</math> , <math>\frac{2}{3}</math> , <math>\frac{1}{4}</math> , ...?
 
 
 
== Problem I7 ==
 
 
 
[[2013 PMWC Problems/Problem I7|Solution]]
 
 
 
All the perfect square numbers are written in order in a line: 14916253649...
 
 
 
Which digit falls in the 100th place?
 
 
 
== Problem I8 ==
 
 
 
[[2013 PMWC Problems/Problem I8|Solution]]
 
 
 
A team of four children are to be chosen from 3 girls and 6 boys. There must be at least one girl in the team. How many different teams of 4 are possible?
 
 
 
== Problem I9 ==
 
 
 
[[2013 PMWC Problems/Problem I9|Solution]]
 
 
 
The sum of 13 distinct positive integers is 2013. What is the maximum value of the smallest integer?
 
 
 
== Problem I10 ==
 
 
 
[[2013 PMWC Problems/Problem I10|Solution]]
 
 
 
== Problem I11 ==
 
 
 
[[2013 PMWC Problems/Problem I11|Solution]]
 
 
 
== Problem I12 ==
 
 
 
[[2013 PMWC Problems/Problem I12|Solution]]
 
 
 
== Problem I13 ==
 
 
 
[[2013 PMWC Problems/Problem I13|Solution]]
 
 
 
== Problem I14 ==
 
 
 
[[2013 PMWC Problems/Problem I14|Solution]]
 
 
 
== Problem I15 ==
 
 
 
[[2013 PMWC Problems/Problem I15|Solution]]
 
 
 
== Problem T1 ==
 
 
 
[[2013 PMWC Problems/Problem T1|Solution]]
 
 
 
== Problem T2 ==
 
 
 
[[2013 PMWC Problems/Problem T2|Solution]]
 
 
 
== Problem T3 ==
 
 
 
[[2013 PMWC Problems/Problem T3|Solution]]
 
 
 
== Problem T4 ==
 
 
 
[[2013 PMWC Problems/Problem T4|Solution]]
 
 
 
== Problem T5 ==
 
 
 
[[2013 PMWC Problems/Problem T5|Solution]]
 
 
 
== Problem T6 ==
 
 
 
[[2013 PMWC Problems/Problem T6|Solution]]
 
 
 
== Problem T7 ==
 
 
 
[[2013 PMWC Problems/Problem T7|Solution]]
 
 
 
== Problem T8 ==
 
 
 
[[2013 PMWC Problems/Problem T8|Solution]]
 
 
 
== Problem T9 ==
 
 
 
[[2013 PMWC Problems/Problem T9|Solution]]
 
 
 
== Problem T10 ==
 
 
 
[[2013 PMWC Problems/Problem T10|Solution]]
 

Latest revision as of 14:09, 20 April 2014

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