Prof. Templeton
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Everything posted by Prof. Templeton
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Six faces but not necessarily square or equal dimensions. So yes all the kiwi boxes are originally stacked into a hexahedron. The boxes themselves are also not necessarily cubes, but hexahedrons.
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Long before Professor Templeton started his career at Redrum University he had a job working in the warehouse of the Manhattan Fruit Exchange. One morning he arrived at work to find that an overhead oil line had begun to leak onto a stack of Kiwi boxes. The oil had leaked along the top of the stack and run down the sides and onto the floor where the uneven surface allowed it to run underneath as well. The boxed Kiwis were stacked into a cube (not necessarily of equal dimensions) and all the boxes on the outside of the cube were now stained with oil while all the boxes on the inside were fine. The Prof. was told to separate the damaged boxes from the undamaged boxes and get a count for insurance purposes. When the Prof. was done he noted that the separated piles were of equal quantities and less than 500 boxes remained undamaged. How many boxes were there to start with?
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That was it.
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For Christmas my kids had received a set of 26 wooden blocks, one for every letter of the alphabet. While playing with my children I would make various shaped towers and walls out of the blocks that they took great delight in demolishing. During one of my building sprees I was thinking back to stacking oranges and wondered if I could make a square pyramid out of the blocks. Certainly I could make one with a 3x3 base, but that would only need 14 blocks, leaving a lot of unused blocks. After some thought I made a square pyramid with a 4x4 base that ended with 1 block on top using only the blocks I had available (which my daughter promptly kicked into oblivion with much glee). How would such a structure be built?
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You should always preform a search when posting riddles or puzzles that are not of your own creation. This is a popular site and there is a good chance that they have already been posted. A search for "birthday +probability" would have listed this topic. I had just posted a variation about social security numbers the other day that also linked to the original. Welcome to the den and I hope to see more submissions.
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Given this stated question I don't believe you have your equation worded correctly. It should be P(A|B) = probability of A (both children are girls) given probability of B (at least one of them is a girl), which when the correct numbers are plugged in becomes P(A|B) = P(A ∩ B)/ P(B) = ¼ / ¾ = 1/3 Same equation, but the set-up is key. I'm sure you would agree that there a 1/4 chance that both children are girls (GG out of GG,BG,GB,BB) and a 3/4 chance that there is at least one girl (GG,BG,GB). So the correct and only answer must be 1/3. QED I hope my html character entities show up properly. Prime would be proud.
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Absolutely. I should have put that into the OP.
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Professor Templeton sat at his desk at the Redrum University updating his students grades into the school computer. Every time he needed to access a student's information he had to enter the last four digits of their social security number. It was a necessary but boring task and so his mind began to wander. The Prof. sat thinking about some of the past brain teasers he had seen on Brainden and was remembering one in particular when he stopped mid-keystroke with a thought. If he had 119 students, how probable was it that the last four digits of a social security number would be duplicated?
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Before I saw the pictures you had posted all my sketches looked like this one above. When I saw yours, I had assumed I interpreted the puzzle wrong. Didn't give it more then a couple of tries before work intruded, however.
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I never would have guessed it if you hadn't done your post first. I was thinking of only classic literature characters. To you goes the assist.
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I wasn't implying that boxcars should be counted twice. I was just stating the obvious (not to some). On 36 possibles a "six" shows up 12 times, 1/6 as expected. If you were told "at least one of the die shows a six", then there are 11 possible scenarios and of those 11 only 2 can total "seven". I completely agree with Scraf on this one.
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Well, I kind of meant cubed in a case of some sort.
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The key is in "at least one". Eleven cases remain, but in one of those cases six must appear twice (boxcars). so a six shows up 12 times out of 72 or 1/6 of the time.
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Side-puzzle: If the oranges had arrived in a perfect cube (any quantity except 1 of course), could a square pyramid have been created with no left-overs?
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Long before Professor Templeton started his career at Redrum University he had a job as a stockboy at the Manhattan Fruit Exchange. One morning a large pallet of oranges arrived that Prof. Templeton was tasked with stacking into a display. When the oranges arrived they were laid out in a perfect square on the pallet. When the Prof. was done he had stacked them all into a four sided pyramid with none left over. Wiping the sweat from his brow, the Prof. marvelled at the fact that he had used all the oranges when making his pyramid and he wondered how that was possible. He knew that there had to have been over 3,000 oranges but surely no more than 6,000. How many oranges, exactly, had arrived to be stacked that morning?
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I'll take a go at it. I've been known to bust a rhyme or two, this game looks like it's very fun to do. 1. Jrod 2. reaymond 3. Lemonymelon 4. ST 5. andromeda - Yippee!!! 6. Limeliam 7. pw0nzd 8. 9. Prof. Templeton 10. 11. 12. 13. 14. 15.
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