Math Forum / Mathematics / Recreational Math / May 2007

48 = 47+1 = 3*2^4 and 54 = 53+1 = 2*3^3. Are there other pairs of
successive primes p and q such that p+1 and q+1 have exactly same
set of prime factors.

What is the probability that a row in a sudoku solution
will look like 465|321|798, in which each successive digit
triplet {1,2,3}, {4,5,6}, {7,8,9} occurs together in of the
three 3-cell sub-rows of the row?  

A bird sits in a rather large locked cage.  An accurate and very precise
scale measures the weight of the cage containing the bird.  The bird takes
flight.  While the bird is in the air does the weight given by the scale
change?

I'm not a professional mathematician, so my efforts can be called
recreational.
Years ago I got a paper published, and sci.math'ers went after it, and
got it retracted by the journal editors with some emails.  The journal

Consider the popular Powerball game take 5 out of 53.
For each set of five numbers one can calculate a std.dev.
E.g. for an 'average' number like 5-15-26-37-49 the
sample std.dev. is 17.40.

I'm looking for a formula that meets certain criteria, and I can't
think of it myself.  The criteria are as follows:
f(0)=0.
f(1)=0.5.

I am looking for an equation that behaves like a sin or cos function,
but doesn't use any trig functions in the actual equations, and x
cannot be an exponent.  no i.  i have been looking for this for a
while now and no one seems to know what it is.

I realized after posting, it is too simple and would appear almost
silly to ask. From the figure, we have 2a =IO^2 / OC - OC, related to
the power of the circle with respect to pole.
However, identification/recognition of an Invariant, which is quite

Six alloy bars each have a cuboid shape with integer dimensions making a total of 18 consecutive measurements in any order. The resultant casting is a cube of integer side length. What are the smallest dimensions of the original bars, and what the cube can be ?

<Warning: I don't have an answer for this, my calculus of variations it too
rusty>
When race cars go into a corner, they start at the outside of the track, and
in mid-corner they're at the inside of the track, then after they leave the

Fifth grade Math Superbowl question:
Let A,B,C,D,E,F,G,H,I represent unique digits from 1 -> 9.
If  ABCD X E = FGHI, then what numbers do the letters represent?
Actually, I'm trying to figure this out for my daughter, so would

Good Morning!
Sometimes the answers to my puzzles cannot be found without the help of a
computer. I sometimes forget though that not everyone is an expert in
computer programming. Therefore, this week, as a special training excercise,

15 consecutive primes:
4010803176619
4010803176649
4010803176719

Find five rectangles whose dimensions are chosen from the integers
1-10 (using each integer only once) that can be put together to form a
square.
Please show me the dimensions of these 5 rectangles

Hello all computer algebra buffs,
None of the current generation computer algebra systems can
simplify this expression directly
6*sin(Pi/14)*(1+sqrt(14-3*sqrt(21))