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.
Half an equilateral triangle
Source: Maths Jam
What is the shortest straight line which bisects an equilateral triangle?
Marbles
Source: UKMT Senior Maths Challenge 2014
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?
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.
If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about crossnumbers, or a random puzzle.
puzzles about crossnumbers, or a random puzzle.