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Posts under Mathemagic

Changing Places

Posted by Chris under Logic, Mathemagic (11 Responds)

A group of 10 people are seated at a circular table. They hadn’t noticed that they had places designated for them, and none of them sat in the right place. Prove that simply by rotating the table, that at least 2 of them can be sat in the right place.

123456

Posted by Chris under Mathemagic (7 Responds)

What is the smallest factor of 123456! + 1?
That number is approximately 2.6 * 10574964

Bordered mat

Posted by Chris under Mathemagic (10 Responds)

I’ve purloined this from the old site.
A table mat is made from red and white beads. There is an inner rectangle made entirely using white beads. It has a border (on all four sides) made from a single layer of red beads. Which mats can have as many white beads as red beads?
All the beads [...]

A complex sum

Posted by Chris under Mathemagic, MathsChallenge (5 Responds)

Evaluate Sum(n = 0 to ∞, cos(n x)/2^n), where cos(x) = 1/5.
Indirect hint, really an excuse to point out the remarkable proof of a distant cousin to the above problem, see: http://en.wikipedia.org/wiki/Gaussian_integral

Intersection of 2 Rectangles

Posted by rajesh under Mathemagic (12 Responds)

Give the formula for the coordinates of the intersecting rectangles formed by two separate rectangles in 2D space ?

Maths Challenge 9

Posted by Chris under Mathemagic, MathsChallenge (23 Responds)

An investor puts $10,000 into a weekly trading scheme.
In each week it is equally likely that he’ll make an 80% gain or a 60% loss (there are no other possibilities). One year later (52 weeks), roughly how much money does the investor expect to have?  The answer is one of the following:
a) $1.95, b) $14,000, c) $140,000, [...]

Maths Challenge 8

Posted by Chris under Mathemagic, MathsChallenge (9 Responds)

Prove that for any natural number that ends in 1, 3, 7 or 9, that it has an infinite number of multiples which consists only of a string of 1’s.
e.g. 13*8547 = 111111
NB It is trivial to show that numbers ending in 0, 2, 4, 5, 6 or 8 cannot possses that property.

Walkies

Posted by Chris under Logic, Mathemagic, MathsChallenge (45 Responds)

A boy, a girl and a dog go for a 10 mile walk. The boy and girl can walk at 2 mph and the dog can trot at 4 mph. They also have a bicycle which only one of them including the dog (it used to work in a circus, OK) can use at a [...]

Bug walk

Posted by Chris under Mathemagic, MathsChallenge (24 Responds)

Four bugs are at the four corners of a square of side length D. They start walking at constant speed in an anticlockwise direction at all times directly towards the bug ahead of them.
How far does each bug walk before they meet with each other?

Sharing marbles

Posted by Chris under Mathemagic (9 Responds)

A group of children share marbles from a bag. The first child takes one marble and a tenth of the remainder. The second child takes two marbles and a tenth of the remainder. The third child takes three marbles and a tenth of the remainder. And so on until the last child takes whatever is [...]

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