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ERJ Brainteaser: June

ERJ Brainteaser: June

28 Jun 2024

For some impressive ‘clue-free’ answering, it’s big congratulations to Michele Girardi, Kamila Staszewska, Andrew Knox and David Mann, new joint holders of the Brainiac of the Month title

Question 3: Three triangles

504 396 ???
H G D K L C

Answer: Extra kudos this week to Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy, who came up with the correct answer 324 (see Solutions below) before any clues were issued. He was followed during the week by: John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Wong SiauWoon, R&D manager, gloves company, Malaysia. Well done to all and everyone else who had a go.

SOLUTIONS

Michele Girardi

As can be seen below, each number can be obtained multiplying by 9 the product of the ranks of the letters

504 396 324

H G D K L C

8 7 4 11 12 3

504 = 8*7*9 396 = 4*11*9 324 = 12*3*9

John Bowen

We know a = 1, so B = 2 and so on

504 = 8 x 7 x 9

396 = 4 x 11 x 9

so ??? = 12 x 3 x9 = 324

Kamila Staszewska

504 H G

H=8, F=7, 8x7=56, 504:56=9 (third multiplication factor discovered)

396 D K

D=4, K=11, 4x11=44, 44x9=396

Answer:

L=12, C=3, 12x3=36, 36x9=324

Sudi Sudarshan

The number is derived as follows: 9 * (ordinal position of first letter * ordinal position of second letter)

H = 8, G = 7; 7*8 = 56; 56*9 = 504

D = 4, K = 11; 4*11 = 44; 44*9 = 396

L = 12, C = 3; 12*3 = 36; 36*9 = 324

Andrew Knox

Converting the letters into numbers as suggested, the second row becomes 8 7, 4 11, 12 3

Factoring the 3-digit numbers gives:

504 = 2^3 x 3^2 x 7 = 8 x 9 x 7 = 504

396 = 2^2 x 3^2 x 11 = 4 x 9 x 11 = 396,

whereby the first and last numbers here correspond with the letters.

Assuming 9 is common to all the middle numbers and that the letters/corresponding numbers beneath each 3-digit number are indeed their factors, then the last number would be 12 x 9 x 3 = 324.

Wong Siau Woon

504

H = 8

G = 7

8 x 9 = 72

504 / 7 = 72

xxx

396

D = 4

K = 11

4 x 9 = 36

396/11 = 36

xxx

L = 12

C = 3

12 x 9 = 108

? / 3 = 108

? = 108 x 3 = 324

New teaser on Monday

Question 2: Tough teaser

12 + 11 = 68

10 + 9 = 52

8 + 7 = 36

6 + 5 = 24

4 + 3 = 12

2 + 1 = ?

Clues: Prime...

Answer: Seems like the harder they come, the harder they fall, as a select number of our top Brainiacs swatted this ‘tough’ one away with ease – especially Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and David Mann, Polymer Business Development (retired), UK; who answered well before any clues were issued. They were followed soon after by: Kate Burns, senior technologist and regulatory officer, Prisma Colour Ltd, Birch Vale, High Peak, Derbyshire; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy and John Bowen, consultant, Bromsgrove, UK. Well done to all and everyone else who had a go.

SOLUTIONS

Kamila Staszewska

The numbers of the right are sum of consecutive prime numbers; numbers on the left denote the order number in prime sequence.

e.g. 12th prime is 37 and 11th prime is 31, sum of which 37+31=68.

Therefore 2nd + 1st prime is 3+2=5.

Andrew Knox

These are sums of pairs of numbers in a list of the first 12 prime numbers:

i.e. 1st & 2nd = 2 + 3 = 5, the first 12 prime numbers being 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

David Mann

Not so tough. It looks like the sums of pairs of the first 12 prime numbers (not counting 1)

12 + 11 (37+31) = 68

10 + 9 (29 + 23) = 52

8 + 7 (19 + 17) = 36

6 + 5 (13 + 11) = 24

4 + 3 (7 + 5) = 12

2 + 1 (3 + 2) = 5

Kate Burns

2 + 1 = 5

The series is the sum of pairs of prime numbers (3+2, 7+5, 13+11, 19+17…), where the numbers in the sum refer to the nth prime number, i.e. 1=2, 2=3, 3=5 etc.

Sudi Sudarshan

My answer to this week's clue: 5

Solution: The equations are in the form:

m-th prime + (m-1)-th prime = n

The first several prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41, ...

12th prime + 11th prime = 37+31 = 68

10th prime + 9th prime = 29+23 = 52

8th prime + 7th prime = 19+17 = 36

6th prime + 5th prime = 13+11 = 24

4th prime + 3rd prime = 7+5 = 12

2nd prime + 1st prime = 3+2 = 5

Stephan Paischer

The answer is 5.

It is the sum of the 1st and 2nd prime number: 2 + 3 = 5

And further, the 3rd and 4th: 5 + 7 = 12 etc.

Michele Girardi

Hi there,

The answer is 2 +1 = 5 , the key is that the addends are the ranks of the prime numbers :

1,2,3, 4, 5 ... correspond to 2,3,5,7,11, etc.

Question 1: Neat numbers

4 = 46, 5 = 521, 6 = 612, _?_,

Answer: Proved a bit trickier than expected for readers to identify the answer 7=343 (see Solutions below). Extra well done, so, to: Simon Winfield, director, MacLellan Rubber Ltd, Wednesfield, Wolverhampton, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.

SOLUTIONS

Simon Winfield

The next numbers in the sequence are 343, 215 and 927

The numbers shown are their cube values reversed.

4 x 4 x 4 = 64 reversed = 46

5 x 5 x 5 =125 reversed = 521

6 x 6 x6 = 216 reversed = 612

7 x 7 x 7 = 343 reversed = 343

8 x 8 x 8 = 512 reversed = 215

9 x 9 x 9 = 729 reversed = 927

Amparo Botella

Neat number is the cube of the number, what means that: