superprismatic

I was born and raised in the state of Delaware. The entire time I lived there, the only method of execution in that state was hanging. My father told me a little-known fact about its use: In Delaware, they cannot hang a person with a wooden leg. Do you know why?

I submit that Mumbles140's answer is by far the most reasonable answer given the usual English interpretation of the problem as it was stated.

Thanks for the NEBRASKA correction (I got the N right!). The US constitution gives the state legislatures the power to appoint electors. As such, they may not voluntarily give up this constitutional power. However, all state legislatures have decided to go with their constituents votes as far as electors are concerned. But they can change their minds at any time, even after the popular election -- Florida was about to do this in 2000 when the Supreme Court ruling made this moot. As far as the OP is concerned, I said "Assuming this process...." which referred to the popular vote to choose electors.

We get rid of the condition that all voters must vote, which was in the Electoral College Puzzle, to make this new puzzle. Everything else is the same. In this new version you can assume as few or as many votes as you like in any state, up to its population. How does this change the answer? I restate the problem with this new change in bold: We all know that it is possible for a presidential candidate to win the U.S. presidency with fewer voters voting for him than for his opponents. That's what this puzzle is all about. In case you need a refresher, here's how the process works: Each state (as well as Washington D.C.) has a number of electoral votes (EVs). The candidate with the most votes in that state (or D.C.) gets all of its electoral votes1. The candidate who gets at least 270 EVs wins. Assuming this process, that the number of voters in each state is its entire population, and that not all voters need to actually vote, what is the fewest number of voters which a winning candidate can have voting for him? 1Footnote: Two states, Nevada and Maine, can split their votes amongst the candidates. For the purpose of this puzzle, assume that they can't. Assume the numbers, below, which will be used for the 2012 election: STATE EV POPULATION ----------------------------- California 55 37253956 Texas 38 25145561 New York 29 19378102 Florida 29 18801310 Illinois 20 12830632 Pennsylvania 20 12702379 Ohio 18 11536504 Michigan 16 9883640 Georgia 16 9687653 North Carolina 15 9535483 New Jersey 14 8791894 Virginia 13 8001024 Washington 12 6724540 Massachusetts 11 6547629 Indiana 11 6483802 Arizona 11 6392017 Tennessee 11 6346105 Missouri 10 5988927 Maryland 10 5773552 Wisconsin 10 5686986 Minnesota 10 5303925 Colorado 9 5029196 Alabama 9 4779736 South Carolina 9 4625364 Louisiana 8 4533372 Kentucky 8 4339367 Oregon 7 3831074 Oklahoma 7 3751351 Connecticut 7 3574097 Iowa 6 3046355 Mississippi 6 2967297 Arkansas 6 2915918 Kansas 6 2853118 Utah 6 2763885 Nevada 6 2700551 New Mexico 5 2059179 West Virginia 5 1852994 Nebraska 5 1826341 Idaho 4 1567582 Hawaii 4 1360301 Maine 4 1328361 New Hampshire 4 1316470 Rhode Island 4 1052567 Montana 3 989415 Delaware 3 900877 South Dakota 3 814180 Alaska 3 710231 North Dakota 3 672591 Vermont 3 625741 Washington D.C. 3 601723 Wyoming 3 563626 ----------------------------- 50 States+D.C. 538 308748481 [/code]

Nice, quick work, guys. Especially to magician who got the technique and k-man who was the first to get the correct answer.

But that's only 21.8% of the votes! If I were the only other candidate, I'd be hopping mad! I'd have lost even though I got 78.2% of the vote! Methinks there's something amiss here!

We all know that it is possible for a presidential candidate to win the U.S. presidency with fewer voters voting for him than for his opponents. That's what this puzzle is all about. In case you need a refresher, here's how the process works: Each state (as well as Washington D.C.) has a number of electoral votes (EVs). The candidate with the most votes in that state (or D.C.) gets all of its electoral votes1. The candidate who gets at least 270 EVs wins. Assuming this process, that the number of voters in each state is its entire population, and that all voters actually vote, what is the fewest number of voters which a winning candidate can have voting for him? 1Footnote: Two states, Nevada and Maine, can split their votes amongst the candidates. For the purpose of this puzzle, assume that they can't. Assume the numbers, below, which will be used for the 2012 election: STATE EV POPULATION ----------------------------- California 55 37253956 Texas 38 25145561 New York 29 19378102 Florida 29 18801310 Illinois 20 12830632 Pennsylvania 20 12702379 Ohio 18 11536504 Michigan 16 9883640 Georgia 16 9687653 North Carolina 15 9535483 New Jersey 14 8791894 Virginia 13 8001024 Washington 12 6724540 Massachusetts 11 6547629 Indiana 11 6483802 Arizona 11 6392017 Tennessee 11 6346105 Missouri 10 5988927 Maryland 10 5773552 Wisconsin 10 5686986 Minnesota 10 5303925 Colorado 9 5029196 Alabama 9 4779736 South Carolina 9 4625364 Louisiana 8 4533372 Kentucky 8 4339367 Oregon 7 3831074 Oklahoma 7 3751351 Connecticut 7 3574097 Iowa 6 3046355 Mississippi 6 2967297 Arkansas 6 2915918 Kansas 6 2853118 Utah 6 2763885 Nevada 6 2700551 New Mexico 5 2059179 West Virginia 5 1852994 Nebraska 5 1826341 Idaho 4 1567582 Hawaii 4 1360301 Maine 4 1328361 New Hampshire 4 1316470 Rhode Island 4 1052567 Montana 3 989415 Delaware 3 900877 South Dakota 3 814180 Alaska 3 710231 North Dakota 3 672591 Vermont 3 625741 Washington D.C. 3 601723 Wyoming 3 563626 ----------------------------- 50 States+D.C. 538 308748481 [/code]

As the setup for this problem is the same as for my earlier post, Shyster Al's Furniture Emporium, I'll repeat the setup: Shyster Al owns a furniture store. He's always looking for a way to lure customers away from his competitors. But, in the cut-throat furniture business, the best deal a dealer can give to a customer is a 25% discount below the MSRP (Manufacturer's Suggested Retail Price) and still make the necessary profit to keep the store viable. One fine day, Al hit on a beautiful scheme for his SAFE (Shyster Al's Furniture Emporium) store which makes it seem as though his customers can get something close to a 33.333...% discount. His scheme is this: If a customer buys several items, he pays full MSRP price for the first item. For subsequent items, he pays full price minus 1/3 of what he had to pay after the discount due on the previous item. For example, if a customer is buying 4 items with these MSRPs, in order, $600, $650, $900, and $300. He pays full price for the first item but gets a discount of $200 on the second item (1/3 of $600) for which he pays $450. This gives him a $150 discount on the third item (1/3 of $450) which costs him $750. So, 1/3 of his net cost of the third item ($250) will be his discount on the fourth, which will now only cost him another $50. So, he pays $1850 ($600+$450+750+$50) for $2450 MSRP of furniture. Each discount is limited by the price of the item being bought, so, e.g., a discount of $100 on something costing $50 will revert to a $50 discount. What is the largest percentage discount which can be realized on 10 items, each having a positive MSRP, bought from Shyster Al? For simplicity, assume that MSRP prices can be any positive real numbers and that all calculations are done with infinite precision. In other words, assume an ideal world where currency is concerned. The answer to my first Shyster Al post was close to 25%. Is this the largest possible for any set of 10 real MSRPs in any order?

Nana7, Dej Mar, and Peekay got it correct to within some small rounding differences. Nice job (and quick)!

Shyster Al owns a furniture store. He's always looking for a way to lure customers away from his competitors. But, in the cut-throat furniture business, the best deal a dealer can give to a customer is a 25% discount below the MSRP (Manufacturer's Suggested Retail Price) and still make the necessary profit to keep the store viable. One fine day, Al hit on a beautiful scheme for his SAFE (Shyster Al's Furniture Emporium) store which makes it seem as though his customers can get something close to a 33.333...% discount. His scheme is this: If a customer buys several items, he pays full MSRP price for the first item. For subsequent items, he pays full price minus 1/3 of what he had to pay after the discount due on the previous item. For example, if a customer is buying 4 items with these MSRPs, in order, $600, $650, $900, and $300. He pays full price for the first item but gets a discount of $200 on the second item (1/3 of $600) for which he pays $450. This gives him a $150 discount on the third item (1/3 of $450) which costs him $750. So, 1/3 of his net cost of the third item ($250) will be his discount on the fourth, which will now only cost his another $50. So, he pays $1850 ($600+$450+750+$50) for $2450 MSRP of furniture. Each discount is limited by the price of the item being bought, so, e.g., a discount of $100 on something costing $50 will revert to a $50 discount. Also, all amounts are rounded to the nearest cent. Now, you wish to minimize what you will pay for 10 pieces of furniture with MSRPs of $487, $403, $315, $289, $262, $252, $233, $229, $208, and $198. In which order should you place these items so as to minimize your cost?

Please explain.

No, you're not missing something. Now try A Funky Weighing Puzzle II.

Suppose you see before you 10 identical-looking blocks. No two of these blocks weigh the same. Your task is to sort the blocks according to weight using the fewest number of weighings. You get to chose which scale you would like to use for all the weighings. The scales are labeled S2, S3, S4, S5, S6, S7, S8, and S9. Once you choose a scale, you must use it exclusively. If you choose scale SN (where N is between 2 and 9 inclusive), then it will only weigh a subset containing precisely N blocks. The scale will then sort the N blocks according to weight and report this weight- ordering to you. What value of N will allow you to determine the weight-ordering of all 10 blocks in the fewest number of weighings?

Suppose you see before you 10 identical-looking blocks. No two of these blocks weigh the same. Your task is to sort the blocks according to weight using the fewest number of weighings. For any given weighing, you are free to use any one of eight scales labeled S2, S3, S4, S5, S6, S7, S8, and S9. Scale SN (where N is between 2 and 9 inclusive) works by taking precisely N blocks, sorting those blocks by weight, and reporting to you their weight-ordering. What is the fewest number of weighings needed to determine the weight-ordering of all 10 blocks?