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Sunday Afternoon Maths XXXV

 Posted on 2014-11-23 

Odd squares

Source: Maths Jam
Prove that 1 and 9 are the only square numbers where all the digits are odd.

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Half an equilateral triangle

Source: Maths Jam
What is the shortest straight line which bisects an equilateral triangle?

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Marbles

A bag contains \(m\) blue and \(n\) yellow marbles. One marble is selected at random from the bag and its colour is noted. It is then returned to the bag along with \(k\) other marbles of the same colour. A second marble is now selected at random from the bag. What is the probability that the second marble is blue?

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37

Take a three digit number where all the digits are the same (eg. 888).
Divide this number by the sum of its digits (eg. 888÷24).
Your answer is 37.
Prove that the answer will always be 37.

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Tags: numbers
If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about pentagons, or a random puzzle.

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