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Second Epsilons

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This is our second collection of stage 5 epsilons. An epsilon problem is quick to read and understand. They might not be so easy to solve!

Epsilons will be good for filling spare mathematical moments. Why not carry a few around with you? (Our first collection of epsilons are here).

Ab Surd Ity
problem
Favourite

Ab Surd Ity

Age
16 to 18
Challenge level
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Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
Biggest Bendy
problem

Biggest Bendy

Age
16 to 18
Challenge level
filled star filled star filled star
Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
BT.. Eat your heart out
problem

BT... Eat Your Heart Out

Age
16 to 18
Challenge level
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If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

Baby Circle
problem
Favourite

Baby Circle

Age
16 to 18
Challenge level
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A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Three Ways
problem

Three Ways

Age
16 to 18
Challenge level
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If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

Upsetting Pitagoras
problem

Upsetting Pythagoras

Age
14 to 18
Challenge level
filled star filled star empty star

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2