Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
All tangled up
problem

All tangled up

Age
14 to 18
Challenge level
filled star filled star empty star
Can you tangle yourself up and reach any fraction?
Polycircles
problem

Polycircles

Age
14 to 16
Challenge level
filled star filled star filled star

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Oddly
problem

Oddly

Age
7 to 11
Challenge level
filled star filled star filled star
Find the sum of all three-digit numbers each of whose digits is odd.
A Tilted Square
problem

A tilted square

Age
14 to 16
Challenge level
filled star filled star filled star
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can it be?
problem

Can it be?

Age
16 to 18
Challenge level
filled star filled star empty star
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Bishop's Paradise
problem

Bishop's paradise

Age
11 to 14
Challenge level
filled star empty star empty star
Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?
Least of All
problem

Least of all

Age
16 to 18
Challenge level
filled star empty star empty star
A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
Difference Dynamics
problem

Difference dynamics

Age
14 to 18
Challenge level
filled star empty star empty star
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Pentanim
game

Pentanim

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.