Indices

There are 41 NRICH Mathematical resources connected to Indices
Rachel's Problem
problem

Rachel's problem

Age
14 to 16
Challenge level
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Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
Largest Expression
problem

Largest expression

Age
14 to 16
Challenge level
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Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?
Thirty Six Exactly
problem

Thirty six exactly

Age
11 to 14
Challenge level
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The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Elevens
problem

Elevens

Age
16 to 18
Challenge level
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Add powers of 3 and powers of 7 and get multiples of 11.
Mega Quadratic Equations
problem

Mega quadratic equations

Age
14 to 18
Challenge level
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What do you get when you raise a quadratic to the power of a quadratic?
Public Key Cryptography
article

Public key cryptography

An introduction to coding and decoding messages and the maths behind how to secretly share information.
Learn About Number Bases
article

Learn about number bases

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
Card Shuffle
article

Card shuffle

This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.
Sums of Squares and Sums of Cubes
article

Sums of squares and sums of cubes

An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.