Algebra: Some kids discovered that if they got on a coin scale two at a
time and one-by-one exchanged places, they could weigh all pairs on one
quarter then figure the weight of each. There are 5 kids and the paired
weights are 129, 125, 124, 123, 122, 121, 120, 118, 116, and 114 lbs
respectively. What is the individual weight of each kid?
From Sam Loyd in Riddles of the Sphinx
Answer available
November 23,
next
puzzle
Answer to math puzzle of
November
9
Algebra: How many polynomials are there of the form x
3 - 8x
2
+ cx + d = 0 such that c and d are real numbers, and the three roots of
the polynomial are distinct positive integers?
From NCTM
Solution: In any cubic polynomial (=0) with 3rd order coefficient = 1,
the opposite of the second-order coefficient (8) is the sum of the 3
roots. The only sets of 3 distinct positive integers which add to 8 are
1+3+4 or 1+2+5. The polynomials are either the product (x-1)(x-3)(x-4)
or the product (x-1)(x-2)(x-5)
For
more math puzzles, check out
http://www.mathpuzzle.com/,
http://mathschallenge.net/,
http://www.princeton.edu/~mathclub/puzzles4.html
and
http://mathforum.org/k12/k12puzzles/
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