Algebra: 4 positive real numbers are such that they form an arithmetic
sequence. The same 4 numbers, with the third omitted form a geometric
sequence. If the 4 numbers in order are a,b,c,d, what is the ratio b/c?
Answer available January 9,
Answer to math puzzle of December 26, 2011
Special Christmas series: On the first day of Christmas, my true love
gave to me an interesting problem: How many presents in total are in the
song? 1 partridge in a pear tree ..... 12 TIMES! 2 turtle doves 11
times. and so forth. How many in 12 days? Generalize: if there were n
days of Christmas, how many presents? Can you justify the formula?
Observed in the news
Solution: 364 (one for every day of the year EXCEPT Christmas!).
If I had received a different kind of gift each day, I would have
received 12 + 11 + 10 + ... + 2 + 1 = 78 ( also known as the 12th
triangular number = (12•13)/2). Instead I get ALL these gifts the 12th
day, all the first 11 type gifts the 11th day, etc. Symbolically it
equal to 12•13•14/6 = 364. If there were n days of Christmas with the
same deal, the total would be (n+2)!/(3!(n-1)!) or n(n+1)(n+2)/6. This
is also called a tetrahedral number (like a triangular pyramid of
would I put them all?!!
ęcopyright 2012, Louis
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updated 2 January 2012