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Resources tagged with Other equations similar to Old Nuts:

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Broad Topics > Algebra > Other equations

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Old Nuts

Stage: 5 Challenge Level: Challenge Level:1

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

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One and Three

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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Around and Back

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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Hike and Hitch

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .

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Three Four Five

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.

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Polynomial Relations

Stage: 5 Challenge Level: Challenge Level:1

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

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Hand Swap

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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Root to Poly

Stage: 4 Challenge Level: Challenge Level:1

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

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Our Ages

Stage: 4 Challenge Level: Challenge Level:1

I am exactly n times my daughter's age. In m years I shall be exactly (n-1) times her age. In m2 years I shall be exactly (n-2) times her age. After that I shall never again be an exact multiple of. . . .

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Rudolff's Problem

Stage: 4 Challenge Level: Challenge Level:1

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

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Bang's Theorem

Stage: 4 Challenge Level: Challenge Level:1

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

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Coffee

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

To make 11 kilograms of this blend of coffee costs £15 per kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee... How many kilograms of each type of coffee are used?

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Are You Kidding

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

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Real(ly) Numbers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

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Golden Ratio

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

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In Particular

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11. Then find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers.

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Deep Roots

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

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Agile Algebra

Stage: 5 Challenge Level: Challenge Level:1

Observe symmetries and engage the power of substitution to solve complicated equations.