Weekly Problem 31 - 2016

The diagram shows a grid of $16$ identical equilateral triangles. How many rhombuses are there made up of two adjacent small triangles?

How many routes are there in this diagram from S to T?

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Two of the four small triangles are to be painted black. In how many ways can this be done?

In how many ways can you give change for a ten pence piece?

Can you find the value of t in these equations?

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?

How many ways are there of completing the mini-sudoku?

How many ways are there to make 11p using 1p, 2p and 5p coins?

Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?

Weekly Problem 21 - 2011

How many ways can you paint this wall with four different colours?

Can you find a number and its double using the digits $1$ to $9$ only once each?

Can you find squares within a number grid whose entries add up to an even total?

Can you choose one number from each row and column in this grid to form the largest possibe product?

What could be the scores from five throws of this dice?

The digits 1-9 have been written in the squares so that each row and column sums to 13. What is the value of n?

Weekly Problem 16 - 2016

How many three digit numbers have the property that the middle digit is the mean of the other two digits?

What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?

I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?

Alberta won't reveal her age. Can you work it out from these clues?

How many triples of points are there in this 4x4 array that lie on a straight line?

In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

If all the arrangements of the letters in the word ANGLE are written down in alphabetical order, what position does the word ANGLE occupy?

How many numbers do you need to remove to avoid making a perfect square?

How many different phone numbers are there starting with a 3 and with at most two different digits?

From this sum of powers, can you find the sum of the indices?

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?