ERJ Brainteaser - January
19 Jan 2026
Each month, ERJ sets a weekly brainteaser, with questions of varying degrees of difficulty. Readers supplying the most accurate (and stylish) answers are then considered for the prestigious Brainiac of the Month title.
Question 3: Snookered
Last week’s World Masters snooker tournament in London included a highly unusual run of results in the round-of-16 (see below), with each match won by a score of six frames to two. What was the probability of that happening?
Email your answer: correct replies on Friday.
Snooker Masters Round of 16
Judd Trump (England) beat Ding Junhui (China), 6 points to 2 points
Neil Robertson (Australia) beat Chris Wakelin (England), 6 points to 2 points
Kyren Wilson (England) beat Si Jiahui (China), 6 points to 2 points
John Higgins (Scotland) beat Barry Hawkins (England), 6 points to 2 points
Mark Allen (Northern Ireland) beat Mark Williams (Wales), 6 points to 2 points
Zhao Xintong (China) beat Gary Wilson (England), 6 points to 2 points
Wu Yize (China) beat Shaun Murphy (England), 6 points to 2 points
Xiao Guodong (China) beat Mark Selby (England), 6 points to 2 points.
Question 2: Give me five II
Write a mathematical expression that has the value of exactly 5, using:
Two, and only two, 2s, and
Any mathematical symbols or operation.
Answer: Very well done for the great solutions (see below) from: Andy Longdon, technical sales manager, Ceetak Ltd, Bedford UK; John Bowen, BSc [Hons], CEng, MIMMM, consultant, Bromsgrove, UK; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; John Woods, materials technology consultant, Hanau, Germany; and everyone else who had a go.
Please note: To make things even more interesting, we have introduced ‘Star Answer’ to recognise extra interesting replies from readers. There will some extra points going for this, which will help us in selecting the winners of the prestigious Brainiac of the Month and Brainiac of the Year awards.
SOLUTIONS
STAR ANSWER: John Woods
I was tempted to say that it is obvious if I was inspired by The Big Brother control of thoughts in the George Orwell classic ‘1984’. The central character Winston Smith is informed after his arrest that control over physical reality is unimportant to the Party provided that the citizens of Oceania subordinate their real-world perceptions to the political will of the Party who could dictate that 2 + 2 = 5.
More mathematically, my proposal is:
[ sec arctan 2 ] to the power of 2 = 5
Where arctan is the angle of a right triangle and and secant is the hypotenuse over the adjacent ( I tip my cap to Pythagoreus ).
Andy Longdon
T2 + 2 = 5
Where T is the Triangular Number, equivalent to : Tn = {n(n+1)}/n When n = 2, T2 = {2 * (2 + 1) } / 2 = 3 Add the second 2 and the answer is 5.
Or using the “termial” function notation: n? = 1 + …. + n The additive version of the more common n! factorial operation.
2? + 2 = 5 2? = 1 + 2 = 3 Add the second 2 and the answer is 5.
John Bowen
5 can be achieved using the function T2, which is the Triangulat function of 2. This is a bit similar to Factorial but instead of multiplying we add, so T2 = 1 + 2 =3 so we now have
T2 + 2 = 5
QED
Amparo Botella
Maybe the most closed to 5 can be = 2π-√2≈5.
Kamila Staszewska
The number five is obtained by adding two squared and two to the power of zero.
Sudi Sudarshan
The only thing I could come up with is this:
?22?= 5 (ceiling or round up function).
Question 1: Next numbers
10/4 = 100
30/5 = 150
19/7 = 200
?/? = ?
Answer: Happy New Year to all our readers and a big well done to everyone who got off on the right track with 7/9 = 250 (See solutions below): Andy Longdon, technical sales manager, Ceetak Ltd, Bedford UK; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Dr Kate Burns, senior technologist and regulatory officer, Prisma Colour Ltd, Birch Vale, High Peak, Derbyshire, UK; John Woods, materials chemistry and technology consultant, Hanau, Germany; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; David Mann, polymer business development consultant, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.
SOLUTIONS
Andy Longdon
Sequence is number of days inclusive from 1st January 2026 until date (eg 10th April, 30th May etc), increasing in 50’s. So next in the sequence, 250 days from 1st Jan, would be 7th September (7/9).
10/4 = 100
30/5 = 150
19/7 = 200
7/9 = 250
John Coleman
These all refer to dates and the number of days between them.
Therefore, taking an additional 50 days as per the sequence and applying the relevant date would give 7/9 = 250.
Kamila Staszewska
The question is related to the New Year as well - since 2026 is a common year (not a leap year), the following applies to it:
10/04 is 100th day of the year.
30/05 is 150th day of the year.
19/07 is 200th of the year
The answer is 07/09 which is 250th day of the year
Dr Kate Burns
The numbers are dates and the day of the year, i.e. 10th April (10/4) is the 100th day of the year, 30th May is the 150th day and so on. 7th September is the 250th day of the year, so 7/9=250.
John Woods
The next numbers are 7/9 and 250.
The preceding numbers are the calendar dates corresponding to the 100th , 150th and 200th day of a year ( leap years excepted ). The 7th of September ( 7/9 ) is the 250th day of the year.
Amparo Botella
I got illuminated just now, thinking of a date instead of a number.
So, the reply will be days on the stated date:
April 10th. is the day 100 of the calendar on a non leap year
May 30th. is the day 150 of the calendar on a non leap year
July 19th. is the day 200 of the calendar on a non leap year
Now we're looking for the 250th day of the year.
That brings us to September 7th.
So the solution to this teaser is:
7/9 = 250
David Mann (Welcome back!)
I think these are day numbers so 7/9 = 250
Sudi Sudarshan
My answer to this week's brainteaser:
7/9 = 250
Left hand side numbers are dates in a non-leap year and right hand numbers are the number of days elapsed from the beginning of the year up to and including that date in a non-leap year.
10/4 or April 10th is the 100th day, 30/5 or May 30th the 150th day, 19/7 or July 19th the 200th day and 7/9 or September 7th the 250th day of the year!
