Logic Puzzles in Visual C#

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Appendix A
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Logic Puzzles
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7, and 10. You ll need to add occurrences of some of the prime numbers to also cover 4, 8, and 9. It s suf cient to have 3 occurrences of 2 to get 4 and 8, and it s also suf cient to keep 2 occurrences of 3 to get 9. So, the minimum integer n that quali es can be expressed as 2 2 2 3 3 5 7 1 = 2519.
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Puzzle 2: Round Manhole Covers
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Manhole covers are typically made round as a safety measure. Any way you turn the round cover, it cannot fall into the round manhole because of its geometrical properties. With other geometrical shapes (rectangle, square, and so on), if you turn the cover in a certain way, it can fall into the manhole and endanger the people working there.
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Puzzle 3: Shaking Hands
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Let s start with the person who shook eight hands (call that person P8). All those who shook the hand of P8 (including myself and excluding the spouse of P8) shook at least one hand. Therefore, the spouse of P8 must be the person who shook zero hands (call that person P0). Now, take P8 and P0 out of the equation. You know that the remaining six people shook a known number of hands (exactly one) from the being-excluded couple. So you subtract one from the answers of all remaining individuals. Simply imagine that you re now facing the same puzzle, but with four couples and with the seven individuals besides me replying to my question with the answers 0 through 6. You ll quickly conclude that the ve couples, including me and my wife, shook hands in the following chiastic manner: 8/0, 7/1, 6/2, 5/3, 4/4. Because I asked nine individuals how many hands they shook and I got nine unique answers, my wife and I must be the couple who shook four hands each. Hence, my wife shook four hands.
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Puzzle 4: Then There Were Five
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I ve seen several versions of solutions to this puzzle, but they re essentially all the same. Here s one with a bit of SQL in it: Given the lter expression col1 = 1 and col2 = 3, there are spaces between 1 and and and and and col2. Another version of the solution refers to a restaurant sign that says sh and chips, and the owner wants to replace the spaces between sh and and and and and chips with hyphens.
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Puzzle 5: Arranging Soldiers in a Row
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The key to the solution is that each soldier can put himself between the correct pair of (placed up to then) soldiers without knowing what s on his hat. Assuming you re one of the soldiers, here s the logic you would follow:
If you enter the room rst, simply position yourself somewhere in the room so that the next soldier can see the sign on your hat.
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If you re not the rst one in the room, look at the hats of the soldiers that are already there. If all soldiers have the same sign, stand to the right of the rightmost one in case that sign is a circle and to the left of the leftmost one in case the sign is a square. If some soldiers have a circle and some have a square, squeeze yourself between the two with the different signs.
Puzzle 6: Crossing the Tunnel
Most people try to solve this puzzle by letting person A walk from start to end with each of the others, then walk back alone to pair with the next person. Intuition says that this approach must be the fastest because person A is the fastest. But if you calculate the total time it takes all four people to get to the end, you get 13 minutes. Of course, the pace is dictated by the slowest in the pair. Person A would need to go from start to end three times: with B (2 minutes), C (4 minutes), and D (5 minutes). These walks amount to 11 minutes, plus the two times that person A needs to walk back alone (1 minute per walk), and you get 13. The trick to solving the puzzle is to gure out that you can save most time by letting the two slowest people walk together. Here s the strategy that gets all the people across in 12 minutes:
Persons A and B walk rst from start to end (2 minutes) Person A walks back (1 minute) Persons C and D walk from start to end (5 minutes) Person B walks back (2 minutes) Persons A and B walk from start to end (2 minutes)
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