Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Yih or Luk tsut k'i or Three Men's Morris
game

Yih or luk tsut k'i or three men's morris

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
A Biggy
problem

A biggy

Age
14 to 16
Challenge level
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Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
Unit fractions
problem

Unit fractions

Age
11 to 14
Challenge level
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Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
Not necessarily in that order
problem

Not necessarily in that order

Age
11 to 14
Challenge level
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Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?
Thousand Words
problem

Thousand words

Age
16 to 18
Challenge level
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Here the diagram says it all. Can you find the diagram?
Honey Bees
problem

Honey bees

Age
14 to 16
Challenge level
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How many bees could fly 1000 miles if they had 10 gallons of honey?
Prime sequences
problem

Prime sequences

Age
16 to 18
Challenge level
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This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
Weekly Lies
problem

Weekly lies

Age
11 to 14
Challenge level
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Mr Ross tells truths or lies depending on the day of the week. Can you catch him out?
Online
game

Online

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Without Calculus
problem

Without calculus

Age
16 to 18
Challenge level
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Given that u>0 and v>0 find the smallest possible value of 1/u + 1/v given that u + v = 5 by different methods.