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started23rd Sep 1975
ended15th Jun 1976
last rpt 1980
5 school years
duration20 mins
age rangeAge 11-13
languageenIn English

Mathshow is a BBC schools TV series from the 1970s, covering Mathematics for secondary school pupils.

A series emphasising mathematical concepts through comedy sketches and animation, with plenty of regular characters. The programmes firmly set out to provide "mid-morning humour" in hopes that this would help pupils remember the rules and techniques that were demonstrated, which were a mixture of the traditional (number sequences, multiplication and division) and "modern maths" (probability, maps and coordinates) - one clear topic per episode.

The teacher's notes warned that "some of the programmes show scenes of explicit mathematics," but teachers using the series would probably be most concerned about how to settle down their classes to normal work after watching a comedy programme in the middle of morning lessons. The producer once challenged teachers: "Are you brave enough to use Mathshow?"[1]

The title of the series was all one word and the cause of some confusion - do you pronounce it "Maths-How", like knowhow, or "Math-Show" using the American expression 'math'? More fun was had with the title during the programmes, for example with the character Professor MOTHWASH, and the Square and Triangle who often mused HM, SO WHAT. One preview announced it as "a series with a title likely to provide the only problem for teachers."[2]

The series had its own announcer, generally seen at the beginning and end of each episode, and featured fake news announcements and adverts. The end credits were often integrated with the mathematical theme of the episode in some way, for example appearing in a rectangle whose coordinates have to be calculated, or being reflected, rotated and tessellated.


Like any good comedy sketch show, Mathshow had a range of regular characters who appeared every week, recurring characters who appeared every so often, and other characters who only appeared once. They were all played by three actors. Here are a selection of the Mathshow characters.

The announcer
  • Newton of the Yard (Tony Hughes), a slow-witted police detective conducting mathematical investigations. After Mathshow ended Newton appeared in his own spin-off series, Maths File.
  • Mrs Mopp (Jacqueline Clarke), Newton's busybody cleaner who also has adventures of her own.
  • Doctor Where (Tony Hughes), an adventurer who travels time and space in his PHONIS with companion Sally-Anne (Jacqueline Clarke). The Brigadier (Charles Collingwood) often seeks his help to investigate maths-related evils perpetrated by a Thing from Outer Mathematics (or possibly from "Pure Mathematics"). A well-observed spoof of the contemporary series Doctor Who, starring Tom Baker.
  • Square (Charles Collingwood) and Triangle (Jacqueline Clarke), two very simple animated characters who talk to each other by flashing. They often observe the other sketches and try to make mathematical sense of what is happening.
  • Tall Bird and Short Bird, a music hall double act consisting of two animated birds.
  • Put-upon Welshman Dai (Tony Hughes) in the village hall.
  • Ron and Eth in the cafe.
  • Alpha and Beta, two black and white silent movie characters like Laurel and Hardy, complete with old-fashioned captions and piano music.
  • Professor Mothwash of the Mathshow International Test Centre, who often has government visitors coming to open his latest complex mathematical machinery.
  • Professor Metrovsky, who has a particular interest in the mathematical background to jokes.
Igor & Frank N. Stein
  • The Mathia, tiny animated gangsters who terrorise Sumsville - "home of mathematical freedom, a place where ordinary numbers go about their everyday calculations without fear, a place where 3 and 2 make 5, or 6, or 1". The Mathia consist of Luigi, Giuseppe and Tonio, and their leader Big M. They often make life difficult for an unfortunate Workman.


Quick episode list

# Title Broadcast
1. Follow That Number! 23 Sep 1975
2. About a Metre 7 Oct 1975
3. O for Symmetry! 21 Oct 1975
4. Fair Share 11 Nov 1975
5. A Wry Tangle 25 Nov 1975
6. Spot Check 13 Jan 1976
7. Factor Fiction 27 Jan 1976
8. Cover-Up Story 10 Feb 1976
9. Positively Not 2 Mar 1976
10. Same Again? 16 Mar 1976
11. A Likely Story 27 Apr 1976
12. Place Your Order 11 May 1976
13. Full Up 25 May 1976
14. A Set of Scales 15 Jun 1976

Recordings of all 14 episodes of the series seem to have been kept by the BBC.

Two of the episodes were revised for repeats from 1976 onwards as noted below, but there is only one version of each episode listed in the BBC archive catalogue. I don't know for sure whether these are the original or the revised versions, but it is worth noting that the version of episode 2 (which had one sketch removed in 1976) listed in the archive catalogue is about 1 minute shorter than the other episodes[3].

Num Title Archive Broadcast
1. Follow That Number! BBC 23 Sep 1975
  Maths content: number sequences

Newton of the Yard investigates some numbers which have been mysteriously scrawled on a door: 1, 3, 4, 7, 11. He is puzzled because he doesn't recognise the sequence. Square and Triangle, and the musical Birds, demonstrate that all sequences have rules, and Eth & Ron and Alpha & Beta all discover their own sequences.

Newton visits a drawing room and investigates a calendar. He discovers a number pattern adding 7 each time and a clue: the number 1. He watches a knock-out tournament at a tennis club and sees that the number of competitors at each stage, working backwards, is 1, 2, 4, 8, 16. He finds another clue: the number 2. Finally he visits a public convenience and notices wall tiles in a square formation of 1, 4, 9, 16, 25 and also a clue: the number 3.

Newton returns to his office to study the clues: 1, 2, 3, and wonders whether the number 4 will be next. His assistant rushes in with the next clue: the number 5. Now Newton knows who the culprit is. He goes to confront Fibonacci: "1+3=4, 3+4=7, 4+7=11. Definitely your work."

  • This episode was revised in light of teachers' comments following its initial transmission in 1975. I don't know exactly what was changed though[3].
2. About a Metre BBC 7 Oct 1975
  Maths content: measurement and accuracy

A Caveman has a wooden club which he calls a Lognuf. The Lognuf is seen at various points in history being measured in different ways and to different degrees of accuracy: in Ancient Rome it is one cubit and two palms long, and in a modern museum it is "700mm, give or take 5mm."

Other characters are also measuring things, including Professor Mothwash who uses a one metre ruler to measure a piece of string running from the north pole to the equator; the dastardly Mathia, whose leader Big M instructs them to "clean up the spare measurements" left over from approximation; and a Magician who is able to make 0.1 units disappear from the weight of three balls by rounding. Even the Announcer joins in, as he attempts to measure the length of the programme.

  • This episode was revised for repeats following its initial transmission in 1975. I believe the changes amounted to a slight re-ordering of some scenes, and the removal of a sequence in which Professor Metrovsky claimed that the Longnuf in a museum was a fake because it was 0.06mm too short - perhaps this scene caused confusion to viewers[3].
3. O for Symmetry! BBC 21 Oct 1975
  Maths content: reflective symmetry

Some of the characters cut and fold paper to make symmetrical shapes, including paper policeman and an ink blot shape. Two circus clowns behave symmetrically, and Tom H. Mot obsesses about symmetry. The Triangle thinks she has found a rectangle, but it is just Square and his mirror image. Triangle normally has three lines of symmetry, but she can stretch into a scalene triangle with no lines of symmetry.

Doctor Where has an adventure based on the concept that an object and its image are the same distance from the line of reflection, about "an invisible barrier across which objects vanished when they passed."[4] All of the letters in the "MATHSHOW" title can be reflected and retain their shapes, except for the "S". Finally the birds reflect the end credits.

4. Fair Share BBC 11 Nov 1975
  Maths content: division

The Mathia are plotting to make off with left over numbers. A Solicitor has to distribute £2,650 in one pound notes between 7 inheritors, and slowly begins taking away 7 from 2650 again and again and again. Short Bird does the same sums on his blackboard, but Tall Bird shows him how to take away 700 at a time first, then 70, then 7. He soon works out that there are 378 sevens in 2650, with 4 left over. The Mathia help themselves to the remainder. The Solicitor finally comes to the same result, and he pockets the left over £4.

Mrs Mopp visits the Mathsnax Takeaway Caff in search of 10 Sevens for Mr Newton. The proprietor Perc Entich gives her a pre-packed Seventy to save time. Beta and Alpha have to divide food into two piles: 6 biscuits, 2 oranges, 7 sandwiches (they cut one in half) and finally 3 eggs...

At a bring-and-buy sale, Dai has to distribute 13 metres of floor space between 5 women's stalls. He splits it into 5 equal spaces of 2.6m2 each, so there is nothing left over for the Mathia. When space for an extra stall is needed Dai has to start again splitting into spaces of 2.16m2 - with 0.04 left over that the Mathia hope to claim. But Dai thinks he can use the space more efficiently by over-estimating and trying to give each stall 2.17m2...

5. A Wry Tangle BBC 25 Nov 1975
  Maths content: angles

There are different ways of demonstrating turns and angles. Short Bird's beak is smaller but it can turn more - he can open it wider - and the birds demonstrate different types of angles. Alpha and Beta stand on the spot and make full turns, half turns and quarter turns. A TV astronomer explains how the Babylonians divided the sky into 360 parts so that the Earth moved through one degree in a day. Professor Mothwash isolates a one-degreee sector from a circle in the Mathshow International Test Centre operating theatre.

The Mathia want to "lean on de angles and put de squeeze on de squares." The Workman draws a right angle and while he is away the Mathia lean on it, reducing it to an acute angle. The Workman comes back and tries again, this time marking the right angle with a little square and drawing in the hypotenuse of a right-angle triangle - this foils the Mathia.

Alpha and Beta are star-gazing, Alpha sees that the Moon is at elevation 30° and Beta tells him to turn another 20° to see Jupiter. But Alpha turns in the wrong direction, demonstrating that turns have a sense as well as a magnitude.

6. Spot Check BBC 13 Jan 1976
  Maths content: geometric pattern

Alpha and Beta are cutting out pastry shapes, and Alpha is able to make much better use of the pastry as his cutter tessellates. Q is making tessellations using equilateral triangles; when P arrives he tries to fit together squares and then other regular polygons, but many of them will not tessellate. Professor Mothwash has sent Paddy to the Maths Tyle do-it-yourself shop, run by Tess Ellation, in search of polygons for tessellating. As the Professor is a semi-regular customer Tess offers semi-regular polygons (such as a kite) which she says will tessellate - but she is wrong about some of them.

Doctor Where helps the Brigadier to track down a sinister White Point. He discovers that it always appears two metres from a kerb (on a straight line parallel to the kerb) and three metres from a bus stop (on a circle centred on the bus stop). The White Point can be found where the line and circle intersect - but Sally-Anne may not be aware of the danger...

The short animated film is shown, introduced by Professor Metrovsky, and finally the programme credits form a tessellation.

7. Factor Fiction BBC 27 Jan 1976
  Maths content: divisibility and primes

The programme begins with a news announcement - the number 97 has disappeared. An identikit pictures has been released by the Number Squad and Newton of the Yard is on the case.

Newton and his assistant are investigating on a street. Newton finds that the house numbers on his side of the street are 2, 4, 6, 8, 10, which are even numbers.

Square explains to Triangle what factors are, showing that 2, 3, 4, 6, 8 and 12 are factors of 24. Meanwhile the Minister for Divisibility and Factorisation is visiting the Mathshow International Test Centre factorisation wing to open a new number-sorting machine. Professor Mothwash first introduces the Evens Sorter (labelled "÷2"), and invites the Minister to input the first number. She enters 522 and the computer produces a card reading '522=2×261'. The MITC staff's training enables them to recognise 261 as an odd number, and to prove the point the Professor enters the number into the Evens Sorter, which flashes a 'REJECT' sign. The number is taken to the Threes Sorter instead, and this machine reveals that '261=3×87'. 87 is also put into the Threes Sorter, revealing that '87=3×29'. Square and Triangle discuss whether 29 is a multiple of 3, 4 or 5.

The animated Sergeant 1 orders the numbers 1 to 100 (apart from the missing 97) into a square formation and puts them through the first few stages of an Eratosthenes drill. Professor Metrovsky explains the importance of the number 3 in British jokes.

Newton has moved over to the odd-numbered side of the street and discovers that not only has 97 disappeared, but it has taken the house with it. "Will 3 go into it?" he asks, and his assistant starts dividing 97 by 3. Newton demonstrates the test for divisibility by 3 (add the digits). As the investigation progresses Newton is able to eliminate all the numbers with factors other than themselves and 1, and is left with a list beginning 2, 3, 5, 7, 11, 13... He doesn't like the number 13 at all, and Alpha is also worried about what will happen on Friday 13th.

Realising that 97 is a prime number Newton races to Downing Street. The programme is again interrupted by a newsflash, as the Prime Minister has resigned and the Ministry for Divisibility and Factorisation has taken over the Ministry of Primes...

8. Cover-Up Story BBC 10 Feb 1976
  Maths content: area

Square thinks he has a "bigger area" than Triangle, explaining that "area is the amount of space you cover." Ron thinks that Eth has got more swiss roll than he has, so he unrolls the two slices and compares them. Alpha and Beta have to fit a piece of carpet into a hexagonal space - Beta doesn't think it's possible but Alpha is able to cut and rearrange pieces from the carpet. Later they rearrange the carpet again as a rhombus, and finally rearrange the rhombus back into a rectangle.

Triangle tries to persuade Square that she is just as big as him because they can both be divided into four equal triangles. Square rearranges Triangle as a rectangle, which fits wholly within Square, finally proving the Square is the larger.

Professor Metrovsky measures an area by overlaying a grid of squares and counting the squares which cover the shape. Miss Mopp comes across Newton's "area" file, with a rectangle that has already been divided into squares. She is able to find the area by multiplying the length by the width.

The Mathia sabotage a rectangle that the Workman has drawn by shearing off the sides to make it a parallelogram. The Workman is easily able to restore the rectangle by erasing a triangle from one side of the shape and re-drawing it on the other side.

9. Positively Not BBC 2 Mar 1976
  Maths content: directed numbers (introduction to negative numbers)

A rocket launch counts down to zero - then seems to count back up again. Square and Triangle move left along a number line to zero - "this is as far as these numbers go." But they can extend the number line into negative numbers.

Dai is counting the profits from the bring-and-buy sale in programme 4. He has to take back £5 from each stall to cover the costs, but one lady only took £4. He works out that she has negative one pound, but can't work out what she has done with that money. Square explains that Mrs Morgan owes one pound.

Frank N. Stein asks Igor to lower the temperature of the thing by ten degrees, and Igor works out that 16-10=6. Frank wants the temperature lowered by another ten degrees but Igor can't do that sum. Frank explains that 6-10=-4. Igor has more trouble when Frank wants another ten degrees taken off before his creation is ready, and has to be shown that -4-10=-14. The Magician performs similar sums involving negative numbers.

Back in the village hall Dai finds £3 that he hadn't counted the first time. Adding that to the previous total it turns out that Mrs Morgan made £2 profit.

10. Same Again? BBC 16 Mar 1976
  Maths content: geometric transformations

Q changes a square into a triangle, but P contends that it hasn't changed at all because it still has the same area. A Thief replaces a stolen painting with a fake, but the fake is the wrong shape. Square explains that the paintings are the same if you are interested in size, but not if you are interested in shape. The Thief tries again with a fake painting that is the right shape, but this time it's the wrong size.

Short Bird thinks that two things with identical size and shape are the same, but Tall Bird says they might be different colours. The Thief now has a fake painting that is the same size and shape as the original, but it has been reflected into a mirror image of the real painting. His next attempt is a rotation of the original.

Professor Metrovsky analyses a silent film for mathematical content. It shows Alpha and Beta moving ("translating") and rotating custard pies.

The Thief makes a final attempt to steal the painting, but this time a translation has occurred.

11. A Likely Story BBC 27 Apr 1976
  Maths content: probability

Ron and Eth toss a coin for the last cake. The coin has shown tails for the last four tosses, so when Eth calls tails again Ron is sure he is going to win, because it must be more likely to show heads next time, surely.

The Minister for Chance and Spec has arrived to open the coin-tossing wing of the Mathshow International Test Centre. Things have come a long way since Professor Mothwash used to toss coins by hand, and the Centre now takes every precaution to "eliminate human interference." The professor shows the results of over a million coin tosses, and explains that even though the latest batch of 100 tests produced 83 heads and 17 tails, the overall proportion is still roughly 50% heads and 50% tails.

Dai is constructung a Wheel of Fortune for the village fete, with ten equal sectors numbered 1 to 10. At last year's fete an unfortunate incident lead to the wheel being declared unfair because the sectors were not all equal.

Doctor Where investigates when the Thing plays havoc with probability on Earth - practically every time Sally-Anne spins a roulette wheel the ball lands on 23, and Ministry tests have shown that the probability of a tossed coin showing heads is now roughly 99% - the Doctor is worried that people will be bored to death by the absolute certainty. The Doctor and his companions cut up a newspaper into small pieces, and draw out one word at a time. Because the normal rules of probability do not apply, a meaningful message is produced at first. But as the game continues the message stops making sense, and normal chaos is resumed.

12. Place Your Order BBC 11 May 1976
  Maths content: coordinates

Mrs Mopp is in a shop and asks for soap powder from the fourth shelf up, but she doesn't specify how far along the shelf it is. Square and Triangle discover that you can find any position if you know which column it is in, and which row. A man knows that to find a position you go along first, then up or down. He uses this technique to find his seat in a cinema.

In an expensive boutique, Des Cartes buys his pop star client some coordinates: "two numbers linked together with a comma and packed in attractive brackets." The Birds and Alpha & Beta both discover that the order of the two numbers in a pair of coordinates is important.

Dai is setting out the chairs in the village hall ready for a pantomime, and labels them all with coordinates. Mrs Griffiths calls and tells him to put out extra chairs. Instead of renumbering the rest, he gives the extra chairs coordinates using column 0 and row 0. There is no space in the hall for any more chairs, so any others will have to go outside "in the negatives."

Frank N. Stein and Igor send their creation (which came to life in programme 9) out on a fiendish plan. They direct it by setting coordinates on a display screen, and Frank has to teach Igor about negative coordinates.

A Sergeant-Major drills a set of co-ordinates, using descriptions such as "those whose second coordinate is more than 2" and "those whose two coordinates are equal."

13. Full Up BBC 25 May 1976
  Maths content: volume

Ron & Eth and Square & Triangle ponder volume. Alpha and Beta are packing cans, but Alpha thinks that "cylinders waste space," so he used triangular prisms which can be packed together without leaving gaps.

Paddy from the Mathshow International Test Centre visits Tess Ellation's shop in search of three-dimensional shapes which fill space. Tess shows him several but he chooses the simplest - the cube. Square and Triangle realise that cubes can be used to measure volume, just as squares can be used to measure area. A policeman discovers that the number of cubes stacked together can be counted by multiplication.

Professor Metrovsky is investigating "what's a Greek urn?" He fills it up with water and then empties it into a rectangular tank, and then uses multiplication to find the volume.

At the Test Centre, Professor Mothwash demonstrates that there are 1000 cubic centimetres in a litre. Square and Triangle show that you can change the shape of something without changing its volume.

The Mathia have a dastardly plan to increase the volume of business. They change the order of numbers in a calculation that the Workman is carrying out, but as it was a multiplication the Workman still gets the correct answer. Big M is not happy.

14. A Set of Scales BBC 15 Jun 1976
  Maths content: maps and plans

A policeman observes a plan being made of the television screen, where each length is half of the real length. He points out that the scale (1:2) must be displayed at all times. Elsewhere some soldiers have to scale a brick wall.

Big M announces that the Mathia are going to operate on a big scale. While the Workman is checking the measurements on the plan for a chair the Mathia sneak into the drawing and change the scale from 1:10 to 10:1. The Workman hands the plans to his assistant, who proceeds to make a tiny chair.

Joe and Maggie are looking round Bekonscot Model Village and discussing the scale (1:12). Suddenly Maggie is reduced to one twelfth of her former height. The Brigadier has information that this is something to do with TQ, and Doctor Where surmises that the is involved. As more information is obtained the Doctor and his companions use larger and larger scale maps to locate the Thing responsible. Eventually they track it down in West London, and rush to the spot...



Jacqueline Clarke as Mrs Mopp, Sally-Anne, Triangle, and others
Charles Collingwood as Announcer, Brigadier, Square, Frank N. Stein, and others
Tony Hughes as Fred Newton, Doctor Where, Dai, Igor, and others

Written by David Taft
David Roseveare
Animation Kate Canning
Set Design Ian Watson
Director David Taft
Producer David Roseveare


The series was designed to be shown fortnightly throughout the school year, with five episodes in the autumn term, five in the spring, and four more in the summer. For most of the run episodes were shown first on Tuesday morning at 9:58am, and then repeated in the following week on Thursday morning at 10:25am. Different programmes - including Out of the Past and Near and Far - were shown in the same slots in the intervening weeks.

Mathshow was broadcast every year from 1975-76 to 1979-80, a total of five years, which is a longer life than had originally been envisaged for the series. The actors' contracts had to be extended by one year to allow the repeat run in 1979-80, and a BBC report in 1979 reported that "it is unlikely that a further extension would be granted."[5]

In autumn 1980 the series was effectively replaced by a spin-off, Maths File, featuring the further adventures of Newton of the Yard.


Watch Online Watch a clip on YouTube. Two short, black-and-white clips from broadcasts of the series in Australia have been uploaded to YouTube. These clips are the source of some of the images on this page. The first contains the Doctor Where sketch, and Dai's final dilemma, from the end of episode 11 A Likely Story

Watch Online Watch a clip on YouTube. The first few sketches from the beginning of episode 12 Place Your Order, plus the end credits


Teacher's notes, spring 1978

Extensive booklets of teacher's notes were published to accompany the series.

Containing 32 pages per term they gave full, scene-by-scene descriptions of each episode (which form the basis for the episode guide above) without giving away too many of the jokes and plot twists, and extensive mathematical background notes and suggestions for classroom follow-up work.

In the middle of each notes booklet there were worksheets that could be copied in schools and given out to pupils. One of the worksheets in the summer term notes was a revision quiz to see whether viewers could remember the topics covered by the autumn and spring term programmes.

The notes were written by Alistair McIntosh, "Principal Mathematics Adviser for Leicestershire and formerly Chairman of the General Committee of the Association of Teachers of Mathematics."

There were no separate pupil's booklets or other resources.


Sources & References

  • BBC (1975) Mathshow Teacher's Notes Autumn 1975. London: BBC. ISBN 0 563 13875 0
  • BBC (1977) Mathshow Teacher's Notes Autumn 1977. London: BBC. ISBN 0 563 30078 7
  • BBC (1978a) Mathshow Teacher's Notes Spring 1978. London: BBC.
  • BBC (1978b) Mathshow Teacher's Notes Summer 1978. London: BBC. ISBN 0 563 30379 4
  • BBC (1979) Broadcasting and Mathematics: The contribution of BBC School and Continuing Education Broadcasting from 1958 to 1979. London: BBC. ISBN 0-563-16403-4
  • Pixley, Andrew (2004) 'Bohemian Rhapsody' in Doctor Who Magazine Special Edition #8: The Complete Fourth Doctor Volume 1. Tunbridge Wells: Panini Publishing. ISSN 0963-1275
  • Roseveare, David (1975) 'There were these two Maths teachers walking down the street...' in Mathematics in School vol.4 no.5 September 1975. Harlow: Longman. ISSN 0305-7259 p.17
  • Roseveare, David (1977) 'BBC TV mathematics programmes for 1977-78-79' in Mathematics in School vol.6 no.5 November 1977. Harlow: Longman. ISSN 0305-7259 p.24
  • Visual Education (1975a) 'Educational Broadcasting' in Visual Education April 1975 p.12
  • Visual Education (1975b) 'Educational Broadcasting' in Visual Education August/September 1975 p.11
  1. "Are you brave enough to use Mathshow?" and also the reference to "mid-morning humour" are from Roseveare (1977). Visual Education (1975b) said "it's a mix of 'mainstream modern maths' and more traditional topics."
  2. The preview of the series in Visual Education (1975a) began "A series with a title likely to provide the only problem for teachers."
  3. 3.0 3.1 3.2 BBC (1977) p.1 states "(episodes 1 and 2) have been modified since 1975 in the light of users' comments." My only source to identify the modifications is to compare the episode synopses in BBC (1975) and BBC (1977).
  4. The Mathshow teacher's notes are not very clear about what Dr Where did in his adventure in O for Symmetry! Pixley (2004) p.27 gives some more details "this insert concerned the menace of an invisible barrier across which objects vanished when they passed. A journey in the PHONIS allowed the Doctor to investigate the mirror-image problem."
  5. BBC (1979) p.14 explains that "by the end of 1979-80 the series Mathshow (11-13) will have been on the air for 5 years. Already the contractual arrangements made with the actors have had to be extended by one year and it is unlikely that a further extension would be granted. Furthermore, the nature of the demand at the lower end of the secondary school has probably changed since Mathshow was planned.


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