# 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:*

*The neat number for 4 = 64, if we invert then number we get: 46*

*The neat number for 5 = 125 ……………………………………….. 521*

*The neat number for 6 = 216 ……………………………………….. 612*

*The neat number for 7 = 343………………………………………… 343*

*The missing numbers are: 7=343*

**Michele Girardi**

*The answer is 7=343 .*

*The number on the right is obtained by the cube of the one of the left, reading the digits right to left :*

*4, 64, 46*

*5, 125, 521*

*6, 216, 612*

*7, 343, 343*

**Andrew Knox**

*Answer: 7 = 343*

*Series of ascending integers whereby the answer is the number cubed and then the digits reversed.*

**Kamila Staszewska**

*These are reversed cubes of numbers:*

*4 > 64 > 46*

*5 > 125 > 521*

*6 > 216 > 612*

*Next number and the answer:*

*7 > 343 > 343*

**Sudi Sudarshan **

*4=46, 5=521, 6=612, 7=343, 8=215, 9=927*

*Solution: Right-hand numbers are the cubes of the left-hand numbers with digits reversed.*

*4: 4^3 = 64; digits reversed = 46*

*5: 5^3 = 125; digits reversed = 521*

*6: 6^3 = 216; digits reversed = 612*

*7: 7^3 = 343 ; digits reversed = 343*

*8: 8^3 = 512; digits reversed = 215*

*9: 9^3 = 729; digits reversed = 927*