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Problems for 2/24

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rabbott Posts: 1649	Posted 15:32 Feb 19, 2014 \| Hide that Number. (x + 10x) % x.length = y. Go backwards from y to x. Table Legs.* Do you understand this problem? Given n table legs of differing lengths how much total must be cut from some of the legs so that the table sits level. Presumably the answer requires that the three longest legs be the same length. The first example has lengths of 2000, 3000, 4000. The given answer is 3000. That makes sense if all the legs must be cut to length 2000. But the second example has legs of 2000, 2000, 1999, 2001. Why isn't the answer 1? [The given answer is 4.] Why can't the table sit level if three legs are of length 2000? (Not all legs are required to be the same length.) The third example has legs of length 2000, 2000, 1999, 2001, 1999. It would seem that the answer here should also be 1, which is the given answer. So I'm confused about the second example. Why does the addition of an additional short leg change the answer from example 2 to example 3? Sticks. asks you to group a set of input numbers into subsets so that each subset has the same total. (All the numbers must be used.) If there are multiple ways to do this, select the way in which the sums are smallest -- not the smallest number of sets. The first example has the numbers 5 2 1 5 2 1 5 2 1. These can be grouped as three sets of {5, 2, 1} or as 4 sets {5, 1}, {5, 1}, {5, 1}, and {2, 2, 2}. Since the second grouping results in sets with sums of 6 and the first grouping results in sets with sums of 8, the second grouping is the answer. Formatting Text. Justify text with small gaps. Going Home. Find the set of paths with the smallest total distance from designated starting points to designated ending points on a grid. Every starting point must reach a unique ending point. Bidding Game. Lazarus, A. et. al. "Richman Games" and "Combinatorial Games under Auction Play." The Bidding Game is what the second paper calls a Poorman Game. Dividing. Stamps. Hard Life gives you a graph. You are asked to find the subgraph (subset of nodes) with the largest ratio of edges to nodes. Last edited by rabbott at 13:33 Feb 24, 2014.

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rabbott

Posts: 1649

Posted 15:32 Feb 19, 2014 |

Hide that Number. (x + 10*x) % x.length = y. Go backwards from y to x.

Table Legs. Do you understand this problem? Given n table legs of differing lengths how much total must be cut from some of the legs so that the table sits level. Presumably the answer requires that the three longest legs be the same length. The first example has lengths of 2000, 3000, 4000. The given answer is 3000. That makes sense if all the legs must be cut to length 2000. But the second example has legs of 2000, 2000, 1999, 2001. Why isn't the answer 1? [The given answer is 4.] Why can't the table sit level if three legs are of length 2000? (Not all legs are required to be the same length.) The third example has legs of length 2000, 2000, 1999, 2001, 1999. It would seem that the answer here should also be 1, which is the given answer. So I'm confused about the second example. Why does the addition of an additional short leg change the answer from example 2 to example 3?

Sticks. asks you to group a set of input numbers into subsets so that each subset has the same total. (All the numbers must be used.) If there are multiple ways to do this, select the way in which the sums are smallest -- not the smallest number of sets. The first example has the numbers 5 2 1 5 2 1 5 2 1. These can be grouped as three sets of {5, 2, 1} or as 4 sets {5, 1}, {5, 1}, {5, 1}, and {2, 2, 2}. Since the second grouping results in sets with sums of 6 and the first grouping results in sets with sums of 8, the second grouping is the answer.

Formatting Text. Justify text with small gaps.

Going Home. Find the set of paths with the smallest total distance from designated starting points to designated ending points on a grid. Every starting point must reach a unique ending point.

Bidding Game. Lazarus, A. et. al. "Richman Games" and "Combinatorial Games under Auction Play." The Bidding Game is what the second paper calls a Poorman Game.

Dividing.

Stamps.

Hard Life gives you a graph. You are asked to find the subgraph (subset of nodes) with the largest ratio of edges to nodes.

Last edited by rabbott at 13:33 Feb 24, 2014.