Math Puzzle of the Week
January 2, 2012

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, next puzzle
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 looks like the sum of a sum which is 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 balls). Where would I put them all?!!
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updated 2 January 2012