#OCRMathsPuzzle
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stevemaths.bsky.social
Here's a slight twist on an arithmetic grid for this week's #OCRMathsPuzzle.

Find the values for p and q so that the arithmetic grid below can be completed.

#MathsToday #UKMathsChat #RecreationalMath

@cambridgeocr.bsky.social
210 has 16 factors. Each factor can be placed in the 4 by 4 grid (one factor per cell), so that the sum of each row and the sum of each column equal the given expressions, where p and q are positive integers. Find the values for p and q so that the grid can be completed. Row 1: (4p + q)/(q - p) Row 2: 13p + 9q Row 3: 5 (p + q) Row 4: p + 11q Column 1: p + 2q Column 2: 12p + 8q Column 3: 10p +2q + 6 Column 4: 7p + 6q
June 19, 2026 at 1:21 PM
stevemaths.bsky.social
Here's a nice little challenge to review #Areas, #Sectors, #Trigonometry, #Surds and #Fractions.

#OCRMathsPuzzle #UKMathsChat #MathsToday #RecreationalMath

@cambridgeocr.bsky.social
The diagrams shows a semicircle with centre O enclosed by the equilateral triangle ABC. The diameter of the semicircle touches line AB. AC and BC are tangents to the semicircle at points P and Q. Work out the exact fraction of triangle ABC that is covered by sector OPQ.
June 12, 2026 at 12:46 PM
stevemaths.bsky.social
Welcome back to the second half of the summer term.

Here is today's #OCRMathsPuzzle for your enjoyment.

#MathsToday #UKMathsChat #RecreationalMath
#Geometry #Area #Surds

@cambridgeocr.bsky.social
A rectangle is partially covered by a square, a regular hexagon and an equilateral triangle. The three shapes covering the rectangle just touch where their edges meet. One edge of the square, two opposite vertices of the regular hexagon and one vertex of the equilateral triangle just touch the edges of the rectangle. Work out the exact fraction of the rectangle that is covered by the 3 regular shapes.
June 5, 2026 at 8:42 AM
stevemaths.bsky.social
Here is today's #OCRMathsPuzzle to consider over half term.

Two circles in a rectangle, measures shown in the diagram.

What is the area of the rectangle not covered by the circles.

#MathsToday #UKMathsChat #RecreationalMath
#Area #Pythagoras #Circles
@cambridgeocr.bsky.social
Two circles, with centres P and Q, are drawn on top of rectangle ABCD, Each circle touches two sides of the rectangle, and the two circles touch each other. The radius of circle P is 30 cm. The radius of circle Q is 10 cm. The length of side AD is 64 cm. Work out the area of the rectangle that is not covered by the circles.
May 22, 2026 at 8:57 AM
stevemaths.bsky.social
It's Friday #OCRMathsPuzzle time 🎉.
The graph shows the equations y = x^2 – 10x + 25 and y = 3 + 6x – x^2 drawn on the same axes.

N & M are points on the curves. Which value of x gives the maximum distance between N & M?

#UKMathsChat #GCSEMaths #ALevelMaths #MathsToday
@cambridgeocr.bsky.social
The graphs of two quadratic equations are drawn on the same axes. y=x^2-10x+25 and y=3+6x-x^2 N and M are points on the curves, between the points of intersection. N is vertically above M. Which value of x gives the maximum distance between N and M?
May 15, 2026 at 9:20 AM
stevemaths.bsky.social
Here's our #OCRMathsPuzzle.

The diagram shows a regular octagon partially covered by a square.
The area of the square is 100 centimetres squared.
What is the exact area of the octagon?

#UKMathsChat #MathsToday #RecreationalMath
#Area #Trigonometry #Geometry #Surds
@cambridgeocr.bsky.social
A regular octagon ABCDEFGH is partially covered by a square AEMN. The line AE cuts the octagon into 2 equal sections. The area of the square is 100 cm^2. What is the exact area of the octagon?
May 8, 2026 at 12:26 PM
stevemaths.bsky.social
Here's our #OCRMathsPuzzle for the long weekend.

What area of the circle is not covered by triangle PCB in the diagram below?

#UKMathsChat #MathsToday #GCSEMaths #ALevelMaths #RecreationalMath

@cambridgeocr.bsky.social
A circle is drawn with centre O and diameter AB. Triangle PCB is drawn over the circle. P is on the circumference of the circle. C is on the diameter AB. PC = 16.8 cm, PB = 60 cm and angle PCB is 90 degrees. What area of the circle is not covered by the triangle PCB?
May 1, 2026 at 11:02 AM
stevemaths.bsky.social
Here is the first #OCRMathsPuzzle of the summer term.

Diagram shows a square ABCD with quarter circles drawn with centres at A and B, radius equal to the side length.

What percentage of the square has been covered by the quarter circles?

#UKMathsChat #MathsToday
@cambridgeocr.bsky.social
Diagram shows a square ABCD. Quarter circles are drawn with centres at A and B. The radius of each quarter circle is equal to the side length of the square. What percentage of the square has been covered by the quarter circles?
April 24, 2026 at 10:44 AM
stevemaths.bsky.social
Continuing with the prime theme, here is today's summer inspired #OCRMathsPuzzle.

Each summer symbol in the grid below represents a prime number.
The sum of each row and the sum of each column are given.
Work out the value of each summer symbol.

#UKMathsChat #MathsToday
@cambridgeocr.bsky.social
A 4×4 puzzle grid featuring summer symbols. Each symbol — umbrella, sandals, glasses, or sun — represents a prime number. Each row has a total shown on the right, and each column has a total shown beneath it. Rows (top to bottom, left to right): Row 1: Umbrella, Sandals, Glasses, Sandals. Row total: 282. Row 2: Umbrella, Sandals, Sun, Glasses. Row total: 290. Row 3: Sun, Sandals, Sun, Sun. Row total: 308. Row 4: Glasses, Umbrella, Glasses, Sun. Row total: 292 Columns (top to bottom using the first image in each row): Column 1: Row 1 Umbrella → Row 2 Umbrella → Row 3 Sun → Row 4 Glasses. Column total: 286. Column 2: Row 1 Sandals → Row 2 Sandals → Row 3 Sandals → Row 4 Umbrella. Column total: 280. Column 3: Row 1 Glasses → Row 2 Sun → Row 3 Sun → Row 4 Glasses. Column total: 304 Column 4: Row 1 Sandals → Row 2 Glasses → Row 3 Sun → Row 4 Sun. Column total: 302.
March 20, 2026 at 3:09 PM
stevemaths.bsky.social
Happy Friday 13th.
Here is today's #OCRMathsPuzzle

Arrange the first 16 prime numbers in the grid below (one per cell), so that the sum of each row and the sum of each column equal the given totals.

#MathsToday #UKMathsChat #RecreationalMath
#Arithmetic #PrimeNumbers
@cambridgeocr.bsky.social
Arrange the first 16 prime numbers in the grid below (one per cell), so that the sum of each row and the sum of each column equal the given totals. Row Sums: top to bottom 84, 105, 110, 82. Column Sums: left to right 92, 109, 100, 80.
March 13, 2026 at 10:15 AM
stevemaths.bsky.social
Here is today's #OCRMathsPuzzle.

Several square blue tiles with side length 2 m are arranged as shown below.
Points A, B and C are marked on vertices of the tiles.

What is the area of the triangle ABC?

#UKMathsChat #MathsToday #RecreationalMath
@cambridgeocr.bsky.social
The arrangement of squares is as follows: Taking point A as the origin, with the squares building upwards from the first row. 2 squares on row 1, where A is the bottom left corner of first square. 2 squares on row 2, starting above the 2nd square of row 1. Point B is the bottom right corner of the 2nd square of row 2. 1 square on the row 3, above the 2nd square of row 2. 3 squares on row 4, with the middle square above the square of row 3. 1 square on row 5, above the 1st square of row 4. Point C is the top right corner of the top square.
March 6, 2026 at 12:04 PM
stevemaths.bsky.social
Here's our #OCRMathsPuzzle for today.

The diagram shows rectangle PQRS and equilateral triangle QST.
Rectangle PQRS has height PS = 5 cm and length PQ = 12 cm.
SR and QT intersect at point A.
What is the area of triangle AST?

#MathsToday #UKMathsChat #RecreationalMath
@cambridgeocr.bsky.social
The diagram shows rectangle PQRS and equilateral triangle QST. Rectangle PQRS has height PS = 5 cm and length PQ = 12 cm. SR and QT intersect at point A. What is the area of triangle AST?
February 27, 2026 at 1:34 PM
stevemaths.bsky.social
Here's our final #OCRMathsPuzzle for the half term.

Find the area enclosed by the circle and tangents in the diagram below.

#UKMathsChat #MathsToday #MathSky #iTeachMath #RecreationalMath #GCSEMaths #ALevelMaths #FSMQ
#Area #Circles #Tangents #Triangles #ProblemSolving
@cambridgeocr.bsky.social
The diagram shows a circle, radius r. A and B are points on circle’s circumference, where the length AB is equal to r. Tangents at points A and B meet at point C. Calculate the exact area enclosed by the circle and the tangents in terms of r.
February 13, 2026 at 11:43 AM
stevemaths.bsky.social
First February #OCRMathsPuzzle for your enjoyment.

Place 9 of the 10 digits from 0-9 in the empty boxes below (1 digit per box), so that the algebraic equation and its solution are correct.​

How many possible ways can you find? ​

#MathsToday #UKMathsChat #GCSEMaths
@cambridgeocr.bsky.social
Place 9 of the 10 digits from 0-9 in the empty boxes (1 per box), so that the algebraic equation and its solution are correct. How many possible ways can you find. two digit boxes y plus two digit boxes equals three digit boxes. y equals two digit boxes. ( a two digit number multiplied by y plus a two digit number equals a three digit number, where y equals a two digit number. The nine digits used are all different)
February 6, 2026 at 11:47 AM
stevemaths.bsky.social
Happy Friday #OCRMathsPuzzle.

Place a different #Fibonacci number in each of the green cells of the grid below, so that the sum of each row & the sum of each column equal the given results.

1, 1, 2, 3, 5, 8, 13, ...

#Sequences #Arithmetic #UKMathsChat #GCSE #ALevelMaths
@cambridgeocr.bsky.social
Place a different Fibonacci number in each of the 3 by 3 cells so that the sum of each row and the sum of each column equal the given results. Top row equals 398, middle row equals 657 and bottom row equals 521. Left column equals 322, middle column equals 720 and right column equals 534. The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13 ... and the Fibonacci rule is Fn = Fn-1 + Fn-2
January 30, 2026 at 11:21 AM
stevemaths.bsky.social
Here's our Friday #OCRMathsPuzzle.

Find the exact area of the shaded region of the diagram.

The shaded region of the square is outside of the circle. The 2 shaded regions of the circle are outside the square.

#UKMathsChat #MathsToday #Geometry #RecreationalMath
@cambridgeocr.bsky.social
Diagram shows an overlapping square and circle on a graph: Centre of circle is at the origin (0,0), The side lengths of the square are equal to the diameter of the circle. Find the exact area of the shaded region of the diagram. The points of intersection are at (-3,4), (-3,-4) and (3,-4). The region of the square that is shaded is outside of the circle. The region of the circle that is shaded is outside the square.
January 23, 2026 at 10:59 AM
stevemaths.bsky.social
Here's this weeks #OCRMathsPuzzle.

Place a different prime number in each of the green cells of the grid below, so that the sum of each row and the sum of each column equal the given prime results.

#UKMathsChat #MathsToday #RecreationalMath
#PrimeNumbers #MathsSky

@cambridgeocr.bsky.social
3 by 3 Addition grid. Sum of top row is 359, sum of middle row is 331 and sum of bottom row is 379. Sum of left column is 353, sum of middle column is 349 and sum of right column is 367. Place a different prime number in each of the nine cells of the 3 by 3 addition grid, so that the sum of each row and the sum of each column equal the given prime results.
January 16, 2026 at 11:46 AM
stevemaths.bsky.social
Hope the term has started well.

Here is this week's #OCRMathsPuzzle

A shape is constructed from a regular hexagon with semi-circles on each edge.

The width of the hexagon, PQ in the image, is 12 cm.

Find the exact area of the full shape.

#UKMathsChat #MathsToday

@cambridgeocr.bsky.social
Image as described in text.
January 9, 2026 at 1:31 PM
stevemaths.bsky.social
Happy New Year 🍾

Our first #OCRMathspuzzle of 2026 is below👇

Using each of the digits 1 to 9 once, create a calculation with a total of 2026.

Use whichever operations you wish. How many unique solutions can you find?

Have an amazing 2026!

#MathsToday #UKMathsChat
@cambridgeocr.bsky.social
image as described in text
January 1, 2026 at 12:14 PM
stevemaths.bsky.social
Our final 2025 festive #OCRMathspuzzle for you. ❄️

Replace each snowflake in the boxes below with one of the square numbers from 1 to 81, so that each Christmas wreath contains the sum of the numbers in its four adjacent boxes.

#MathsToday #UKMathsChat #RecreationalMath
@cambridgeocr.bsky.social
Labelling the snowflakes of the boxes in the top row A, B and C. Labelling the snowflakes of the boxes in the middle row D, E and F. Labelling the snowflakes of the boxes in the bottom row G, H and I. The boxes A + B + D + E = 105 for the top left Christmas wreath. The boxes B + C + E + F = 95 for the top right Christmas wreath. The boxes D + E + G + H = 106 for the bottom left Christmas wreath. The boxes E + F + H + I = 75 for the bottom right Christmas wreath.
December 19, 2025 at 12:56 PM
stevemaths.bsky.social
Here's our second festive #OCRMathspuzzle for 2025.🎄

Write each of the multiples of five from 5 to 60 into the baubles on the tree, so that the five baubles along each edge all sum to the same total.

#UKMathsChat #MathsToday #RecreationalMath
#Arithmetic

@cambridgeocr.bsky.social
The image shows a Christmas tree with baubles arranged in a triangular pattern with one bauble at each corner and three baubles along each side. The challenge is to arrange the twelve baubles that have been numbered five to sixty in the five times table so that the sum of the five baubles on each edge add to the same total.
December 12, 2025 at 1:45 PM
stevemaths.bsky.social
Here's our first festive #OCRMathspuzzle of the season. 🎄

Each festive symbol in the grid below represents a prime number.

The sum of each row and the sum of each column are given.
Work out the value of each festive symbol.

#UKMathsChat #RecreationalMath #Arithmetic

@cambridgeocr.bsky.social
The festive symbols across each row and the totals. Row 1: bells, tree, wreath, holly 120. Row 2: wreath, bells, bells, tree 134. Row 3: holly, bells, holly, wreath 114. Row 4: wreath, tree, tree, holly 112. The festive symbols down each column. Column 1 bells, wreath, holly, wreath 122. Column 2: tree, bells, bells, tree 132. Column 3: wreath, bells, holly, tree 120. Column 4: holly, tree, wreath, holly 106.Each festive symbol in the grid represents a prime number. The sum of each row and the sum of each column are given. Work out the value of each festive symbol.
December 5, 2025 at 12:31 PM
stevemaths.bsky.social
Here's the #OCRMathsPuzzle for this week

What fraction of the square’s area is covered by the two quarter-circles?

Have a fantastic weekend 😀

#Area #Circles #Fractions #Algebra #surds

#MathsToday #UKMathsChat #RecreationalMath
@cambridgeocr.bsky.social
Two quarter circles are drawn on square ABCD. One quarter circle is drawn from point A, with an arc from side AB to side AC. The second quarter circle is drawn from point D, with arc from point B to point C. The two quarter circles touch at a single point E inside the square. What fraction of the square's area is covered by the two quarter circles?
November 28, 2025 at 1:15 PM
stevemaths.bsky.social
The #OCRMathsPuzzle for this week is below!

A, B and C are points on the circumference of a circle, centre O.
Angle BAC = 70°
AC = 9 cm
AB = 7 cm

What is the circumference of the circle, correct to 3 significant figures?

#MathsToday #UKMathsChat #Geometry #ProblemSolving
@cambridgeocr.bsky.social
A, B and C are points on the circumference of a circle, centre O. Angle BAC = 70 degrees Length AC = 9 cm Length AB = 7 cm What is the circumference of the circle, correct to 3 significant figures?
November 21, 2025 at 12:40 PM
stevemaths.bsky.social
Here's this week's #OCRMathsPuzzle!

What fraction of the rectangle ABCD is covered by the triangles DPE and CQE?

Have a great weekend!

#UKMathsChat #MathsToday #RecreationalMath #Geometry #Area #Fractions

@cambridgeocr.bsky.social
The image shows rectangle ABCD. Points P and Q are on the line AB such that AP = PQ = QB. The Length AD = AP. There are lines DQ and CP which intersect at point E. What fraction of the rectangle ABCD is covered by the triangles DPE and CQE?
November 14, 2025 at 12:43 PM