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Tag Archives: Combinatorics
[Soln] Identifying the weight of one ingot
King Hiero II of Syracuse has 11 identical-looking metallic ingots. The king knows that the weights of the ingots are equal to 1, 2, …, 11 libras, in some order. He also has a bag, which would be ripped apart … Continue reading
Identifying the weight of one ingot
King Hiero II of Syracuse has 11 identical-looking metallic ingots. The king knows that the weights of the ingots are equal to 1, 2, …, 11 libras, in some order. He also has a bag, which would be ripped apart … Continue reading
[Soln] 2013 AIME I Problem 6
2013 AIME I 6. Melinda has three empty boxes and 12 textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of … Continue reading
2013 AIME I Problem 6
2013 AIME I 6. Melinda has three empty boxes and 12 textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of … Continue reading
[Soln] 2013 AIME I Problem 4
2013 AIME I 4. In the array of 13 squares shown below, 8 squares are coloured red, and the remaining 5 squares are coloured blue. If one of all possible such colourings is chosen at random, the probability that the chosen coloured array appears … Continue reading
2013 AIME I Problem 4
2013 AIME I 4. In the array of 13 squares shown below, 8 squares are coloured red, and the remaining 5 squares are coloured blue. If one of all possible such colourings is chosen at random, the probability that the chosen coloured array appears … Continue reading
[Soln] 2013 AIME I Problem 2
2013 AIME I 2. Find the number of five-digit positive integers, , that satisfy the following conditions: (a) the number is divisible by 5, (b) the first and last digits of are equal, and (c) the sum of the digits of … Continue reading
2013 AIME I Problem 2
2013 AIME I 2. Find the number of five-digit positive integers, , that satisfy the following conditions: (a) the number is divisible by 5, (b) the first and last digits of are equal, and (c) the sum of the digits of … Continue reading
[Soln] 2016 Japan Math Olympiad Preliminary Problem 10
2016 JMO Prelim 10. Boy A and 2016 flags are on the circumference of a circle, with circumference length 1. He wants to get all the flags by moving on the circumference. Find the smallest possible such that for any position … Continue reading
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