ERJ Brainteaser: December

Question 3: ? ? ?

.-. / . / - / .-. / ?  / ?  / ? /

Answer: Hats off this time to Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain, who answered RETREAD (Morse code: .-. / . / - / .-. / . / .- / -.. ) well before any clues were issued. She was followed soon after by: Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen BSc [Hons], CEng, MIMMM, consultant, Bromsgrove, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Jose Padron, project manager, E2Metrix Canada Inc., Sherbrooke, Quebec, Canada; Andy Longdon, technical sales manager, Ceetak Ltd, Bedford UK. Well done to all, and everyone else who had a go.

Next teaser on 5 Jan 2026 - with the winners of the Brainiac of the Year Awards also to be announced that week.

Wishing all our readers a very Happy Christmas and a great New Year!

First square = 5, second square = ?

Answer: Squaring up nicely this week with the correct answer – 30 – were: Andy Longdon, technical sales  manager, Ceetak Ltd, Bedford UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; John Bowen BSc [Hons], CEng, MIMMM, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Woods, rubber technology consultant, Hanau, Germany; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain;  Bharat B Sharma, technical director TWC Group (Techno Waxchem & Rajsha Chemicals), Kolkata, India; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Tom Jenkins, business development, R.D. Abbott Co. Inc., Garden Grove, California, USA. Well done to all and everyone else who had a go.

SOLUTIONS

Andy Longdon

Answer = 30. Total number of squares that are in the grid.

For a 2 x 2 grid, there are four 1x1 squares and one 2x2 square = 5 total

For a 3 x 3 grid, there are nine 1x1, four 2x2 and one 3x3 = 14 total

For a 4 x 4 grid, there are sixteen 1x1, nine 2x2, four 3x3 and one 4x4 = 30 total.

Kamila Staszewska

The answer should be how many squares can be found within the figure grid. First one has 5 squares (4 singles + 1 double) and second has 16 singles + 9 doubles + 4 triples + 1 quadruple = 30 squares in total.

John Bowen

The number given for the 2x2 square is 5, the total number of squares [4x1, + 1 2x2]

For the 4x4 square, we have

16x1

9 x2x2

4 x3x3

1 x4x4

Total 30 squares

Andrew Knox

Answer: second square = 30

30 is the total numbers of squares of sides 1 unit (16), sides 2 units (9), sides 3 units (4) and sides 4 units (1).

Sudi Sudarshan

The number for each figure represents the total number of squares.

Number of squares in the first figure: 4 squares of length 1 unit + 1 square of length 2 units  = 4 + 1 = 5

The second figure has:

16 squares of length 1

9 squares of length 2

4 squares of length 3

1 square of length 4

Total number of squares = 16+9+4+1 = 30

General rule: For an nxn square grid, the number is  n^2 + (n-1)^2 + ... + 3^2 + 2^2 + 1^2

John Woods

The first square  = 5 which is composed of :

4 squares of dimension 1 x 1

 and

1 square of dimension 2 x 2

-> 5 squares

The second square = 30 which is composed of :

1 square of dimension 4 x 4

4 squares of dimension 3 x 3

9 squares of dimension 2 x 2

16 squares of dimension 1 x 1

Amparo Botella

I think the result is the following one:

1st. square =  4 small 1×1 squares + 1 big 2x2 squares = 5

2nd square = 1×1: 16 + 2×2: 9 + 3×3: 4 + 4×4: 1 = 30

In 2x2 square grid, there are 5 squares (given answer)  which is 4 small and 1 big square.

Bharat B Sharma

 In a 4x4 grid *the question, There will be 30 different squares (considering all sizes of squares)squares)

1x1  as 16 squares

2x2 as 9 different squares

3x3  as 4 different  squares

1 as the whole grid (4x4 square) .

The answer, therefore, is that the second square (4x4 grid) has total of 30 (16+9+4+1) different squares as explained above.

Tom Jenkins

Second square:

1x1 squares = 16

2x2 squares = 9

3x3 squares = 4

4x4 squares = 1

Total = 30

New teaser on Monday.

Find the rubber connection in: Egypt, Laos, Austria, Spain, Thailand, Oman, Mexico, Ecuador, Rwanda.

Answer: We do try to avoid sending readers on a ‘wild goose chase’, so apologies if that was the case for anyone this week. Many thanks for all the imaginative, alternative ideas, but the solution here is simply that the first letter of each country-name spell the word ELASTOMER. Very well done to: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Antonella Pagliarulo, product development manager, performance polymer solutions, Thomas Swan & Co. Ltd, Consett, County Durham, UK; John Woods, consultant, Germany; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; John Bowen BSc [Hons], CEng, MIMMM, consultant, Bromsgrove, UK; Andy Longdon, technical sales  manager, Ceetak Ltd, Bedford UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.

New teaser on Monday.