 Puzzle thread Nov. 10 |
Mon, 10 November 2003 20:29  |
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 Ron |
 | Commander
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Location: Collegedale, TN | |
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Here are this week's puzzles:
Several are more IQ style than math style.
1. The term 'Egyptian fraction' refers to those fractions whose numerator is 1 and whose denominator is any other whole number. Example 1/4 , 1/8, 1/27 are all Egyptian fractions.
How can the fraction 19/94 be expressed as the sum of two Egyptian fractions? (find two Egyptian fractions whose sum equals 19/94.
2. The number 1920212223...939495 consists of 154 digits, and was arrived at by placing the numbers 19 to 95 one after the other. If I now remove 95 of the digits (from anywhere in the number) in such a way that the resulting number is the greatest possible, what are the first 19 digits of the 59-digit number that remains?
3. What number should replace the question mark?
6 8 17 21
13 1 9 10
3 15 4 ?
4 6 4 5
4. In the triangle shape below, what number replaces the question mark?
2
7 3
3 ?
5 1 5 6
5. What number comes next in this sequence?
483, 759, 264, 837, 592, ?
I will wait 24 hours before randomly picking the Weekly Puzzle Master from among those who PM me all correct answers. I will not inform those who get wrong answers, but will post the correct answers here after the deadline.
Thread locked until deadline over.
[Updated on: Tue, 11 November 2003 07:59]
Ron Miller
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| Re: Puzzle thread Nov. 10 |
Tue, 11 November 2003 23:12  |
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| LEit |
 | Lt. Commander |
Messages: 879
Registered: April 2003
Location: CT | |
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| Ron wrote on Tue, 11 November 2003 21:34 |
3. 6 is the missing number. In each vertical column, the sum of the 3 smaller numbers equal the larger number.
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I got 2:
With 2, the sum of the columns is: 26, 30, 34, 38.
The sum of the rows is: 52, 33, 24, 19. The differences are 19, 9, and 5, which fits a pattern of 2x-1.
I thought there was a fair chance I was following the wrong pattern however. How can you tell which pattern is the one the puzzle wants?
- LEitReport message to a moderator
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| Re: Puzzle thread Nov. 10 |
Wed, 12 November 2003 00:43 |
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Thank you - thank you 
1. Simple mathematics: 1/x + 1/y = 19/94. From this I extracted a formula for
y, saw that the minimum for x would be 5 (otherwise y would be negative),
tried 5, and calculated y to be 470.
2. As the total digits you'll be left with is fixed, the chore is to get as
many 9s in front. First remove the 1, then 4x19 to get 4 more 9s. You're then
left with removing 18 still, so you can't get another 9, so settle for 8
(from the 68). 1 more to remove, so that's another 6 (from the 69), and
you'll end up with the correct answer.
3. Took me a little while to realize that the highest number in each column
equalled the sum of the other three.
4. A hunch really: saw a triangle, and figured the sum in each diagonal would
be equal, and found it to be correct.
5. This one took me the longest. I tried just about every mathematical
connection between the numbers I could think of; couldn't find any, so tried
to find a connection between the numbers, and suddenly saw it was just a
pattern of 8 digits repeating itself....
Ash
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| Re: Puzzle thread Nov. 10 |
Wed, 12 November 2003 08:33 |
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| Ron |
| Commander
Forum Administrator
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| LEit wrote on Tue, 11 November 2003 23:12 |
I thought there was a fair chance I was following the wrong pattern however. How can you tell which pattern is the one the puzzle wants?
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Sorry folks... I'm using a book, and don't have the time (or maybe the spare brain cells) to look for possible alternate answers other than the answer given in the book.
Using the alternate answer of 2, both LEit and BlueTurbit got all the answers correct.
When you sent in your answers to me, some of you mentioned how you figured each puzzle out. This is a good idea, as it lets me know if a puzzle has an alternate answer that I was not aware of. I can then update the puzzle post, specifying that there are more than one answer for a certain question.
So, I apologize to LEit and BlueTurbit for not noticing that an there was an alternative answer for question 3, and I will do better next time.
Since I've already awarded Ashlyn this week's Puzzle Master status, it would not be good to take it away from her to run the random number program. It's my mistake for not noticing/accepting the alternative answer, and hopefully LEit and BlueTurbit will be gracious enough to forgive me and wait for their turn next week.
Ron Miller
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| Re: Puzzle thread Nov. 10 |
Wed, 12 November 2003 14:15 |
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| BlueTurbit |
| Lt. Commander
RIP
BlueTurbit died Oct. 20, 2011 |
Messages: 835
Registered: October 2002
Location: Heart of Texas | |
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The Egyptians didn't use negative numbers. 
Fractions not numbers in Euclid; Archimedes worked with fractions, Diophantus regarded them as numbers (as opposed to magnitudes in Euclid). No negative numbers in classical mathematics.
Negative numbers start to appear; big boost by invention of analytic geometry (Descartes, Fermat): true roots vs. false roots
There cannot be of course a negative number without the presence of a zero; however, in Europe, the mathematicians have the zero since the XIV century, and it will be necessary to await the end of the XV century to see appearing non-positive numerical beings, which therefore will not be accepted like numbers with whole share.
An author of a handbook of mathematics, XIX century, (F Busset), will go as far as making carry the failure of the teaching of mathematics in France to the admission of the negative quantities. He is shocked that it is discussed if there exist "quantities smaller than nothing ". It is for him " the roof of the aberration of human reason ".
http://nti.educa.rcanaria.es/penelope/uk_confboye.htm
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| Re: Puzzle thread Nov. 10 |
Wed, 12 November 2003 15:09 |
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Very interesting reference...
Sort of goes against the grain of some basic premises which I use in the teaching of binary mathematics to my students...
"Subtraction IS Addition, it is simply the addition of a negative number."
"Division IS Multiplaction, it is simply the multiplication of an inverse number."
Going to have to think about that.
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