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| == Problem I1 ==
| | The following is a list of [[PMWC]] problems from the year 2013 |
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| [[2013 PMWC Problems/Problem I1|Solution]] | | *[[2013 PMWC Problems|Entire Exam]] |
| | | *[[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?
| | **[[2013 PMWC Problems/Problem I1|Problem I1]] |
| | | **[[2013 PMWC Problems/Problem I2|Problem I2]] |
| == Problem I2 ==
| | **[[2013 PMWC Problems/Problem I3|Problem I3]] |
| | | **[[2013 PMWC Problems/Problem I4|Problem I4]] |
| [[2013 PMWC Problems/Problem I2|Solution]] | | **[[2013 PMWC Problems/Problem I5|Problem I5]] |
| | | **[[2013 PMWC Problems/Problem I6|Problem I6]] |
| Given that ''A'', ''B'', ''C'' and ''D'' are distinct digits and
| | **[[2013 PMWC Problems/Problem I7|Problem I7]] |
| | | **[[2013 PMWC Problems/Problem I8|Problem I8]] |
| A A B C D - D A A B C = 2 0 1 3 D
| | **[[2013 PMWC Problems/Problem I9|Problem I9]] |
| | | **[[2013 PMWC Problems/Problem I10|Problem I10]] |
| Find A + B + C + D.
| | **[[2013 PMWC Problems/Problem I11|Problem I11]] |
| | | **[[2013 PMWC Problems/Problem I12|Problem I12]] |
| == Problem I3 ==
| | **[[2013 PMWC Problems/Problem I13|Problem I13]] |
| | | **[[2013 PMWC Problems/Problem I14|Problem I14]] |
| [[2013 PMWC Problems/Problem I3|Solution]] | | **[[2013 PMWC Problems/Problem I15|Problem I15]] |
| | | **[[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.
| | **[[2013 PMWC Problems/Problem T2|Problem T2]] |
| | | **[[2013 PMWC Problems/Problem T3|Problem T3]] |
| == Problem I4 ==
| | **[[2013 PMWC Problems/Problem T4|Problem T4]] |
| | | **[[2013 PMWC Problems/Problem T5|Problem T5]] |
| [[2013 PMWC Problems/Problem I4|Solution]] | | **[[2013 PMWC Problems/Problem T6|Problem T6]] |
| | | **[[2013 PMWC Problems/Problem T7|Problem T7]] |
| == Problem I5 ==
| | **[[2013 PMWC Problems/Problem T8|Problem T8]] |
| | | **[[2013 PMWC Problems/Problem T9|Problem T9]] |
| [[2013 PMWC Problems/Problem I5|Solution]] | | **[[2013 PMWC Problems/Problem T10|Problem T10]] |
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| Find the sum of all the digits in the integers from 1 to 2013.
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| == Problem I6 ==
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| [[2013 PMWC Problems/Problem I6|Solution]] | |
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| What is the 2013th term in the sequence
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| <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> , ...?
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| == Problem I7 ==
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| [[2013 PMWC Problems/Problem I7|Solution]] | |
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| All the perfect square numbers are written in order in a line: 14916253649...
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| Which digit falls in the 100th place?
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| == Problem I8 ==
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| [[2013 PMWC Problems/Problem I8|Solution]] | |
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| 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?
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| == Problem I9 ==
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| [[2013 PMWC Problems/Problem I9|Solution]] | |
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| The sum of 13 distinct positive integers is 2013. What is the maximum value of the smallest integer?
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| == Problem I10 ==
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| [[2013 PMWC Problems/Problem I10|Solution]] | |
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| Four teams participated in a soccer tournament. Each team played against all other teams exactly once. Three points were awarded for a win, one point for a draw and no points for a loss. At the end of the tournament, the four teams have obtained 5, 1, ''x'' and 6 points respectively. Find the value of ''x''.
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| == Problem I11 ==
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| [[2013 PMWC Problems/Problem I11|Solution]] | |
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| == Problem I12 ==
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| [[2013 PMWC Problems/Problem I12|Solution]] | |
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| == Problem I13 ==
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| [[2013 PMWC Problems/Problem I13|Solution]] | |
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| == Problem I14 ==
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| [[2013 PMWC Problems/Problem I14|Solution]] | |
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| == Problem I15 ==
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| [[2013 PMWC Problems/Problem I15|Solution]] | |
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| Given that 1 + <math>\frac{1}{2^2}</math> + <math>\frac{1}{3^2}</math> + ... = ''M'' and 1 + <math>\frac{1}{3^2}</math> + <math>\frac{1}{5^2}</math> + ... = ''K'', find the ratio of M : K .
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| == Problem T1 ==
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| [[2013 PMWC Problems/Problem T1|Solution]] | |
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| == Problem T2 ==
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| [[2013 PMWC Problems/Problem T2|Solution]] | |
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| == Problem T3 ==
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| [[2013 PMWC Problems/Problem T3|Solution]] | |
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| == Problem T4 ==
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| [[2013 PMWC Problems/Problem T4|Solution]] | |
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| == Problem T5 ==
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| [[2013 PMWC Problems/Problem T5|Solution]] | |
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| == Problem T6 ==
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| [[2013 PMWC Problems/Problem T6|Solution]] | |
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| == Problem T7 ==
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| [[2013 PMWC Problems/Problem T7|Solution]] | |
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| == Problem T8 ==
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| [[2013 PMWC Problems/Problem T8|Solution]] | |
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| == Problem T9 ==
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| [[2013 PMWC Problems/Problem T9|Solution]] | |
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| == Problem T10 ==
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| [[2013 PMWC Problems/Problem T10|Solution]] | |
