Fred and Sally’s combined age is 65.
Fred is three times as old as Sally was when Fred was the age that Sally is now.
How old are they?
Your Custom Text Here
Fred and Sally’s combined age is 65.
Fred is three times as old as Sally was when Fred was the age that Sally is now.
How old are they?
Fill in all the empty squares of the grid with the digits 1-9, such that:
1: A diamond shape denotes that the four numbers adjacent to it add to 20.
2: Every diamond uses a different way to add to 20, so if for example one diamond is surrounded by 1,2,8,9, no other diamonds can use those same four numbers, not even in a different order.
3: Identical digits are not allowed to occupy adjacent squares of the grid, not even diagonally adjacent.
What is the radius of this circle?
Use the following letter pairs to form a series of words: a 4-letter word, a 6-letter word, an 8-letter word, a 10-letter word and a 12-letter word.
Each of the letter pairs can only be used once, EXCEPT for five of them.
Those five special letter pairs appear at the end of each of the five words, and also earlier in the same word. For instance if the 8-letter word ends in OR, it would need to be either:
(OR----OR), (--OR--OR) or (----OROR).
I have a pair of three-digit numbers that are the reverse of one another, let’s call them abc and cba. The greatest common divisor of abc and cba is 7.
What are the two numbers?
What is the highest number that:
is always a multiple of as long as a and b are integers?
In this figure there are two identical large squares and two identical smaller squares. What is the area of the red triangle in terms of the areas of the squares?
In the above continued fraction, replace the letters a,b,c,d with the numbers 1,4,5,7 in whatever order you wish.
What is the maximum value of x?
The following words all have something specific in common:
SCAR THOU NAPA SOLE TECH DOLL DIVE DIVE GALA
The order they are in is related to the thing they have in common.
DIVE is in the list twice – this is not a mistake.
Which one of the following words also belongs in the list, and where in the list should it be placed?
BECK CLEF PARA PAST
If 32 degrees Fahrenheit = 0 degrees Celsius,
and -40 degrees Fahrenheit = -40 degrees Celsius,
calculate in your head what temperature will be the exact same amount of degrees for each but positive for Fahrenheit and negative for Celsius.
Some quarter circles (and semi circles) are arranged in (and out) of a rectangle as shown. What is the length of the line marked with a question mark?
What number is missing from this sequence?
11, 236, 315, 4384, 5175, ???, 7735, 8128, 9135,
I’ve started with a 3x3 square, and divided it into 9 1x1 squares as shown. I’ve added four 1x1 squares such that for each of them one corner lies on a corner of the central 1x1 square, and the corner opposite that lies outside of the 3x3 square. I’ve used this as the basis of the lower figure, a bizarre 20 sided polygon.
What is the perimeter of this polygon?
A straight line is drawn through a circular array as shown. The line is tangent to the lower left and upper right circles. This line passes through some of the other circles and also passes through the space between the circles.
What proportion of the line is within the circles?
A player plays a Wordle type game, where feedback is given after each guess. The player correctly finds the answer ‘DELAY’ on her fourth guess. Her guesses were:
I S S U E
A L A R M
B I D E T
D E L A Y
At each point the guess could have been the solution, in other words she hasn’t employed any clever elimination tactics. There were still a handful of other possibilities at the point where she got the answer, but it was not unreasonable that she guessed it after four guesses given the feedback she had.
What feedback was she receiving after each guess?
An extra challenge if you fancy it: find another word that still might have been the answer after the first three guesses, with the feedback as it would have been for DELAY.
Still on the subject of kites, it is straightforward to dissect a regular pentagon into five identical kites as shown. If the kites all need to be different however, as far as I can tell you need at least 7 kites to make up a regular pentagon. But how might you do it?
We are using the definition that kites must be convex, with two pairs of identical sides located adjacently (as opposed to a parallelogram where the identical sides are opposite). A hint: a rhombus is allowed as a special case of a kite.
It is possible to dissect ANY non-square rectangle into one square and four DIFFERENT non-square kites. How?
(A kite is defined as a quadrilateral with two pairs of identical sides, with the identical sides adjacent – unlike a rectangle where the identical sides are opposite).
Lines are drawn from each corner of a rectangle, tangent to a circle as shown. The lengths of three of these lines are 10, 6 and 15. What is the length of the fourth line?
Joshua and Leoni have been next-door neighbours for the past 34 years
In 1990, Joshua’s age was the sum of the digits of Leoni’s age.
In 2024, Joshua’s age is the sum of the SQUARES of the digits of Leoni’s age.
How old were they and are they?
Eight unit squares are placed within a right-angled isosceles triangle as shown.
What is the area of the triangle?