# Only Ones

Using any or all of the operations of addition, subtraction, multiplication, division and exponentiation (and brackets), and as many of the number 1 as you need, produce each of the numbers from 2 to 20. For example, here is one way to make the number 17: $latex (1+1+1)^{(1+1)} \times (1+1) -1=17$ What is the smallest … Continue reading Only Ones

# One Spot Dice

You have two blank 6-sided dice. You are allowed to choose any number of the twelve faces and draw exactly one dot on each of those faces. Now roll both dice. Can you draw the dots so that the possible totals are equally likely? Extension Put dots on several faces of two 6-sided blank dice. … Continue reading One Spot Dice

# Number of Letters

The numbers seven, eleven, fifteen, nineteen make a sequence where the numbers go up by 4 each time. But if you count the number of letters in each word, you get a sequence of numbers that goes up by 1 each time – 5, 6, 7, 8. The list above has 4 numbers in it. … Continue reading Number of Letters

# Lousy Labelling

Three boxes filled with lots of balls are on the table. One box is full of red balls, one is full of blue balls, and one is filled with both red and blue. Three labels are made for the boxes, but they are stuck to the wrong ones so that no box ends up with the right label. You can’t see what colour the balls in each box are unless you pull some balls out to look. How many balls do you need to pull out of the boxes to know which box is which?

# Area Maze #5

Find the pink area.

# Combo Cube

Eight cubes are marked with one dot on two opposite faces, two dots on two opposite faces and three dots on two opposite faces. The eight cubes are glued together to form a bigger cube. The dots on each face of the large cube are counted, to get six totals. Can the cubes be arranged … Continue reading Combo Cube

# Area #9

Find the purple area.

# Area #9

Find the area of a star formed in an octagon placed on an equilateral triangle.

# One Truth, Two Lies

Two straight lines, AB and CD, are on the same plane. One, but only one, of the following statements is true: AB and CD are parallel AB and CD are not perpendicular AB and CD intersect Which statement is it?

# Area #7

FInd the exact value for the purple area within the dodecagon. Note: Not for the faint-hearted.