What is the area of the smallest quadrilateral that can enclose three non-overlapping circles, two of which have radius 72 and one of which has radius 98?
Puzzle of the Week #571 - Crossing Triangles
Two large equilateral triangles are overlaid as shown to form six smaller equilateral triangles and a hexagon.
The areas of the triangles are given, what is the area of the hexagon?
Puzzle of the Week #570 - Cube
A point in space outside of a cube is the following distances from four of the vertices of the cube.
What is the side length of the cube?
Puzzle of the Week #569 - Two Chords in a Quarter Circle
What is the radius of this quarter circle?
(Drawing not to scale).
Puzzle of the Week #568 - Dice
I have a standard six sided dice marked 1,2,3,4,5,6. Since the probability of rolling a 6 is 1/6, if I keep rolling till I get a 6 it would take on average 6 rolls.
How many rolls on average would it take to roll a six if I only consider sequences of rolls that DON’T contain any 1s?
Puzzle of the Week #567 - Basketball Tournament
Seven teams took part in a basketball league tournament. Each possible pair of teams either played each other once or twice.
After the end of the tournament the coach of the Nuneaton Predators asked the other six coaches how many games their teams had each played, and was surprised to receive six different answers.
How many games did the Nuneaton Predators play?
Puzzle of the Week #566 - Central Area
A rectangle is divided into four regions as shown. Three of the regions each have an area of 1.
What is the area of the central region?
Puzzle of the Week #565 - Parts of Circles
A quarter-circle and a third-of-a-circle are placed together on a baseline as shown. A line is drawn between the far vertices of the two shapes, such that the two red line segments are equal.
What are the relative areas of the quarter-circle and the third-of-a-circle?
Puzzle of the Week #564 - Comparea
In this figure, comprising a square and two circles, which of the two shaded areas is larger?
Puzzle of the Week #563 - Powers
a+b = s
a*b = p
What is a^4 + b^4 in terms of s and p?
Puzzle of the Week #562 - Zig Zag Sequence
I’ve constructed a sequence thusly:
I’ve started with the natural numbers 1,2,3,4,5,6,7,8,9,10 etc.
I’ve kept the first number as it is, then reversed the order of the next two, then reversed the order of the subsequent three, then reversed the order of the next four etc:
1,3,2,6,5,4,10,9,8,7,15,14,13,12,11,21,etc
Your task is to construct a formula that will instantly give you the nth term in this crazy sequence.
Puzzle of the Week #561 - Four Circles in a Triangle
Four circles are tangent to a triangle and to one another as shown. If a fifth circle is drawn enclosing the second and third circles, that circle is the same size as the fourth circle in the triangle.
If the smallest circle has radius 1, what is the radius of the second smallest circle?
Puzzle of the Week #560 - Concentric Circles
Puzzle of the Week #559 - Minimal Combinations
I have 2k items and I select k of them. There are N possible combinations that I could have selected. N is a multiple of 1000. What is the smallest k could be?
Puzzle of the Week #558 - Isosceles Trapezoid
Here is an isosceles trapezoid, a shape with two parallel sides and the other two sides are equal. I have drawn two lines within the shape to split it into three regions of equal area. What is the overall area of the trapezoid?
Puzzle of the Week #557 - Palindromic Numbers
I learned the interesting fact the other day that any natural number, however large, can be written as the sum of at most three palindromic numbers. For instance, 7369 = 7227+131+11.
Can you write the ten digit number 7,275,640,031 as the sum of three palindromic numbers?
Single digit numbers count as palindromes (eg, 7) but numbers with leading zeroes do not (eg 0330).
Puzzle of the Week #556 - Triangle and Semicircle
In this figure, what is the height of the triangle?
Puzzle of the Week #555 - Regular Nonagon
Here is a regular polygon with nine sides. If two of the regions have areas 3 and 2 as shown, what is the area of the third region?
Puzzle of the Week #554 - Fiftieth Birthday
If a person is born at a random point in a 400 year period, roughly what is the probability that their fiftieth birthday will be on the same day of the week as they were born?
Puzzle of the Week #553 - Unknown Primes
(2+1/a)(2+1/b)(2+1/c) = d
a, b, c and d are all prime numbers, what are they?