ERJ Brainteaser: April

N12, E3, S6, ?

Answer: Some neat replies to this week’s teaser, with a little bit of humour also thrown in. The answer is W9 (see Solutions below) and well done to: Simon Winfield, director, MacLellan Rubber Ltd, Wednesfield, Wolverhampton, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; John Bowen, rubber & tire industry consultant, Bromsgrove, UK; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Jim Cristiano, director, category management, HDT Automotive Solutions LLC, Livonia, Michigan, USA: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Kate Burns, senior technologist and regulatory officer, Prisma Colour Ltd, Birch Vale, High Peak, Derbyshire; and everyone else who had a go.

SOLUTIONS

Simon Winfield

Answer is W9

These are points on a compass combined with corresponding numbers on a clock face.

John Bowen

Next is W9; replace the numbers on a clock face and transpose to a compass card.

North = 12, East = 3, South = 6, West = 9

John Coleman

The answer is W9 (Orientation representation on a clockface)

Sudi Sudarshan,

Solution: The other elements of the list, namely, N12, E3, S6 represent the cardinal direction and the position of the hour hand that represents the direction. So North 12 O'Clock, East 3 O'Clock, South 6 O'Clock and hence West 9 O'Clock.

Amparo Botella

The result is W9, time in the clock of each cardinal point (north, south, east and west)

Jim Cristiano

Place a compass on top of a clock.  North (N) is at 12 o'clock; East (E) is at 3;00; South (S) is at 6:00.  Therefore, West (W) is at 9:00. 

N12, E3, S6, W9

Andrew Knox

Answer: W9 (By combining a clockface with a compass, whereby 12 is North.

(I was going to answer West, being car park names surrounding the NEC in Birmingham, but your clue "time" ruined that answer...)

Kamila Staszewska

The numbers correspond with the hour marks on an analogue clock dial (12, 3, 6) and the letters represent compass directions (N for North, E for East and S for South).

Therefore, starting from the top moving clockwise: 12N, 3E, 6S and - the answer - 9W.

Michele Girardi

If you superimpose a clock and a compass, you'll get the correspondence between main directions and time:

North 12, East 3, South 6 and West 9

Kate Burns

The answer is W9 – the letters refer to the cardinal directions (North, South, East, West) and the numbers are the corresponding number on a clock face.

Question 2: Odd number

What is the sum of the first 77 odd numbers?

Answer: Well done to the following select group who so neatly (Solutions below) got to the correct answer 5929: Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; John Bowen, rubber industry consultant, Bromsgrove, Worcs, UK; Andrew Knox, Rubbond International, The Netherlands; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA; and everyone else who had a go.

SOLUTIONS

Sudi Sudarshan

My answer: 5929

77th odd number is 77*2-1=153

Sum = 1 + 3 + 5 + ... + 153

= (1+153)+(3+151)+ ...+(75+79)+77

=154*38+77 = 5852+77 = 5929

John Bowen

It can be proved that the sum of a series of n odd numbers starting at 1, = n-squared, so the sum of the first 77, starting with 1 , = 77 x 77 = 5929

Andrew Knox

Answer: 77 squared = 5929

Trying the first few sequences and a simple pattern emerges (without recourse to the Internet).

1 (3) 5 = 9

1 3 ( ) 5 7 = 16

1 3 (5) 7 9 = 25

1 3 5 ( ) 7 9 11 = 36

1 3 5 (7) 9 11 13 = 49

Sum appears to be the square of the middle number (or the "interpolated" middle number if there are an even number of numbers in the sequence).

The last number appears to be 2n -1 so in a sequence of the 77 uneven numbers this will be 153, and the middle number if n is uneven will be n, i.e. in this case 77.

So the sum in this case is the square of 77 = 5929.

Amparo Botella

The last odd number of the 77 first ones is 153 (1,3, 5, 7………  149, 151, 153) and the sum of all of them is: 5929

Peter D. Talbot

First, determine what is the 77th odd number.

77th odd number = (77 X 2) – 1 = 154 – 1 = 153

Attempt to make an even number of pairs using the highest number added to the lowest number in the series.

77 odd numbers will not give a whole number of pairs (38.5).

Therefore, make 38 pairs of odd numbers (1st odd number + 76th odd number, 2nd odd number + 75th odd number etc.) and add the 77th odd number to make the total.

76th odd number is 151.

Each pair of odd numbers total 152 (1 + 151, 3 + 149, 5 + 147 etc.)

Total of 77 odd numbers = (38 X 152) + 153 = 5776 + 153 = 5929

Question 1: Give me five (decimal places)

.1

.04

.001

.0005

.0000?

Answer:  This time it’s hats off to Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA, who came up with the correct answer (see below) before any clues were issued. Very well done also to the following select group, who recognised that these were the first five decimals in Pi: Jim Cristiano, director, category management, HDT Automotive Solutions LLC, Livonia, Michigan, USA: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and everyone else who had a go.

 SOLUTIONS

Sudi Sudarshan

Here is my answer: 9

Solution: The numbers seem to represent the decimal portion of the value of Pi which is 3.141593 to 6 decimal places. The numbers in the sequence are: 0.1, 0.04, 0.001, 0.0005, 0.00009, ... which when added together gives 0.14159 which is the fractional portion of the value of 5 to 5 decimal places.

Jim Cristiano

We are looking at pi: 3.14159.  Therefore the next number is 0.00009.

Amparo Botella

The missing decimal number is 9 = .00009. The 141592 are the decimals of pi number: 3,141592

Andrew Knox

The last single digit in this pyramid is the next digit in Pi (after the decimal place) Pi being 3.1415926.. as I remember it)