Logic Puzzle Day 2005
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by Commius
Hola chicos, final exams are over and its a new new day so time for a new logic puzzle! First the answer to the last logic puzzle:
Answer:
“This problem can likewise be solved in any one of a dozen possible ways -- but in only one good way.
The unimaginative procedure is to laboriously set down one number as 1000a + 100b + 10c + d, and the other as 10,000e + 1,000f + 100g + 10h + i, multiply through and then analyze each individual cross product, starting with the highest. Another possibility is to use the analogy of a rectangle, with each side successively increased to form partial products, realizing that area is greatest when the added rectangles at each step give a total rectangle closest to a square. A third method is to consider the logarithms of the two multipliers, which is similar in reasoning but clumsier in execution than the optimum approach.
Clearly, the simplest solution to which all the others essentially reduce is to apply the familiar rule that if the sum of two numbers is constant, their product increases as their differences decreases. It will be recalled that we readily proved this in our high school algebra days by letting x + y = k, x - y = d, squaring both sides and subtracting, from which 4xy = k^2 - d^2. Since it is evident that the larger digits must be as far to the left as possible, we readily set down the following pairs in succession, applying the rule above, which means that the smaller of the two at a minimum. Note that the final “1” must likewise annex to the smaller number:
9 96 964 9642 9642
8 87 875 8753 87531
Remember to shout and vote this article! The answer will appear in the next article.
Crossing A River
‘A detachment of soldiers must cross a river. The bridge is broken, the river is deep. What to do? Suddenly the officer in charge spots 2 boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold 2 boys or 1 soldier. Still, all the soldiers succeed in crossing the river in the boat. How?
Solve this problem either in your mind or practically -- that is, by moving checkers, matches, or the like on a table across an imaginary river.’
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Rawr! First! Just like ST6!
2nd. voted
One boy can row the boat as well as one soldier or as two boys. Hence always ensure there is a boy on the far shore. So start with a boy on each shore. When a soldier rows over, alone, the boy makes the trip back and forth, bringing the second boy back with him. The second boy then goes to deliver the boat to a waiting soldier on the near shore, restoring the original condition. Repeat.
Or use the boat and oars to fix the bridge.
One soldier rows the boat, the rest hang onto the edge of the boat in the water and get pulled across the river.
1) Boy "A" comes with the boat to the soldiers.
2) Boy "A" stays on the shore, and a soldier gets on the boat to the other shore.
3) Boy "B" comes with the boad to the soldiers and the boy "A".
4) Boys "A" and "B" goes to the other shore with the boat.
And repeat all the levels...
make a bigger bot