There are two fractions, 34/55 and 55/89. We are looking for a third fraction of positive integers a/b, where 34/55>a/b>55/89 and 55<b<89. What is the smallest b where this is possible?
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#337787 SBT Fraction
Posted by BMAD on 14 March 2014  05:30 PM
#337786 semiregular polygons
Posted by BMAD on 14 March 2014  05:19 PM
 1
#337766 Smallest Consecutive Integer Triangle Possible
Posted by BMAD on 11 March 2014  02:41 PM
 1
#337748 checker chase game
Posted by BMAD on 10 March 2014  02:12 AM
 1
#337747 average birthdays
Posted by BMAD on 10 March 2014  02:08 AM
of b+g?
 1
#337746 antifirst
Posted by BMAD on 10 March 2014  01:55 AM
E.g.
1 has 1 divisor,
2 has 2 divisors, (skip 3 since it only has 2 divisors)
4 has 3 divisors,
6 has 4 divisors, and so on...
So the first four numbers are (1,2,4, and 6).
Your tasks,
find the biggest antifirst number under 1,000,000.
Prove or provide a counter example to the following conjecture, all antifirst numbers greater than 6 are abundant or perfect.
 1
#337731 Sheep Mowing service
Posted by BMAD on 07 March 2014  04:47 PM
If we tie a sheep to one peg it eats out a circle in grass. If we put a rope through a ring on its neck and tie both ends of the rope to two pegs it eats out an ellipse. If we want an oval we tighten one rope between two pegs put a ring with a rope on it and tie the sheep to its other end.
How to tie a sheep so that it eats out a square in grass? We have one sheep ropes pegs and rings.
 0
#337678 reversed coefficients
Posted by BMAD on 03 March 2014  06:27 PM
If P(x) and Q(x) have 'reversed' coefficients,
for example:
P(x) = x^{5}+3x^{4}+9x^{3}+11x^{2}+6x+2
Q(x) = 2x^{5}+6x^{4}+11x^{3}+9x^{2}+3x+1
What can you say about the roots of P(x) and Q(x)?
 0
#337677 Simplified American Football
Posted by BMAD on 03 March 2014  06:22 PM
 1
#337676 number theory: 7 conjectures
Posted by BMAD on 03 March 2014  06:12 PM
 0
#337644 Circles to make a pentagon
Posted by BMAD on 01 March 2014  04:15 PM
Remember @Bonanova, we can only use a compass.
 1
#337634 Circles to make a pentagon
Posted by BMAD on 28 February 2014  04:34 PM
tslf, you have me worried. For I have done it much the same way. Let me reexamine my own solution as well.
 1
#337586 scheme
Posted by BMAD on 27 February 2014  03:14 PM
 0
#337544 Complex numbers
Posted by BMAD on 26 February 2014  05:26 PM
 1
#337502 Spin the bottle
Posted by BMAD on 25 February 2014  05:55 PM
6 friends are sitting in a circle whom you have been observing playing the game called 'spin the bottle'. They invite you to play as well. Being a good sport, you agree to play. You happen to notice however that it is HIlga's turn and you would rather not kiss Hilga. You have also noticed that the bottle when spun with the left hand has a tendency to stop on a person an even distance away (e.g. the second, fourth, sixth person from her) and when spun with the right hand will land on a multiple of 3 distance away from HIlga. Currently the bottle is pointing directly across from Hilga but if it were to land on herself she would immediately spin it again from that position, switching hands in the process. You have no idea which hand she will use first nor do you know which way rotation she will place on the bottle [clockwise or counterclockwise].
Where should you sit?
 1
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