ERJ Brainteaser - March

Question 3: Missing country

Complete the list: Brazil, Colombia, Ecuador, Gabon, Republic of the Congo, Democratic Republic of the Congo, Uganda, Kenya, Somalia, Indonesia, ?.

Answer: Some geographic variations in the replies, but key here was to recognise the Equator as the link between these countries. Well done to: Bharat B Sharma, technical director TWC Group (Techno Waxchem & Rajsha Chemicals), Kolkata, India; 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; John Coleman, membership manager, Circol ELT, Dublin, Ireland; John Woods, materials technology consultant, Hanau, Germany;  Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA.

SOLUTIONS

Bharat B Sharma

The list is of countries touching Equator or through which Equator line passes. There are 11 countries and two water bodies (of two countries). 11th country in the list is - Sao Tome and Príncipe. Two countries where the Equator passes but through water- these are – Maldives (passes through water between atolls). Kiribati (passes through Pacific Ocean waters between island)

Amparo Botella

I believe all these countries cross the equator, so the missing country will be Maldivas.

Kamila Staszewska

These are the countries that the Equator passes through on land, and the missing country is Sao Tome and Príncipe.

John Woods

All the countries are crossed by the Equator and the next in the series should be KIRIBATI where the Equator runs through its territorial waters which means that the list should have included Sao Tome and Príncipe and the Maldives. Answer: KIRIBATI as we complete our circumnavigation of the globe.

John Coleman

Answer: Sao Tome and Principe is the 13th country through which the Equator passes through.

Andrew Knox

Answer: Sao Tome and Principe (one country).

These are the 11 countries with land mass through which the equator passes. The Maldives and Kiribati are two further countries but only control water through which the equator passes.

Sudi Sudarshan

My answer: Sao Tome and Principe. Possibly also Maldives and Kiribati. These are countries on the equator going from west to east starting with the Americas. Sao Tome and Principe should be with the African countries. Only the waters of Maldives and Kiribati cross the equator but not their land masses.

New teaser on Monday.

8, 61, 42, ?

Answer: Our top Brainiacs were quick to spot that the numbers shown here are multiples of 8 with digits reversed, making 23 the correct answer – though there were a couple of interesting, alternative interpretations. Very well done to : Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; 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; David Mann, polymer business development consultant, UK; Hans-Bernd Luechtefeld, Consultant, Germany; John Woods, materials technology consultant, Hanau, Germany; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; and everyone else who had a go.

STAR ANSWERS

John Woods

I propose that the numbers are - multiples of 8 which are then inversed

Operation -> Multiples of 8

8 x 1 = 8

8 x 2 =16

8 x 3 = 24

8 X 4 = 32

Operation -> inversion of numbers generated .

8 a single digit , therefore unchanged -> 8

16  -> 61

24 -> 42

And therefore 32 -> 23

The final Number in the Sequence is 23

Hans-Bernd Luechtefeld

The number you are looking for is 23.

Rationale:

1. The sum of digits, starting with 8, then 7, followed by 6, ergo the next should be 5
2. From figure to figure, deduct 2 from the the previous first digit: 8-2=6, 6-2=4, 4-2=2 > the last figure should start with a 3
3. The second digit of the last figures follows the following rule: 8 has no second digit, the second figure has 1, the third figure has 2, then the last one has a 3 as second digit.

Alternatively:

Andrew Knox

Ans:wer: 23

Adding the digits of each number gives 8, 7, 6, and 5 to complete the sequence. The first digit of each number appears to go down by 2, and  the second digit goes up by 1: (0), 1, 2, and then the next should be 3. So 23 fits, but the first number being 8 rather than 80 is of concern, as is the fact that the sequence based on this reasoning does not continue further than 04 as the next number.

Amparo Botella

The next number may be 32, making a series with the sum of numbers, which will be 8,7,6,5:

34, 55, 89, 144, _?_, 377

Answer: Not our toughest ever teaser, perhaps, but extra marks here for everyone who mentioned Fibonacci or even better ‘fibs’. Well done to: 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; John Bowen, BSc [Hons], CEng, MIMMM, consultant, Bromsgrove, UK; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; David Mann, polymer business development consultant, UK;  Jose Padron, project manager, E2Metrix Canada Inc., Sherbrooke, Quebec, Canada; John Woods, materials technology consultant, Hanau, Germany; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Hans-Bernd Luechtefeld, Consultant, Germany.

SOLUTIONS

Amparo Botella

This sequence follows the pattern, that each number is the sum of the two previous numbers.

34 + 55 = 89

55 + 89 = 144

89 + 144 = 233

144 + 233 = 377

Missing number: 233

Final sequence:

34, 55, 89, 144, 233, 377

Kamila Staszewska

These seems to be a series of fibs: 233 is the answer.

34+55=89

55+89=144

89+144=233

144+233=377

John Bowen

This is a Fibonacci series, where each number is the sum  of the previous 2, so the missing number is 233,  so 233 + 144 = 377.

John Coleman

Answer: This sequence follows the Fibonacci sequence, where each number is the sum of the two previous numbers:          

34 + 55 = 89

55 + 89 = 144

89 + 144 = 233

144 + 233 = 377

So the missing number is 233.

Andrew Knox

Answer: 233

Add the two preceding numbers to get the next number.

David Mann

In this sequence the next number is formed by adding the previous number to it.

89 = 55 + 34, 144 = 89 + 55,  so the missing number is 144 + 89 = 233. Then 233 + 144 is, as expected, 377.

John Woods

34, 55, 89, 144, _?_, 377

If we assign each number as N1 , N2 , N3 , N4 , N5 ? and N6 , it seems that ,

N3 = N1 + N2

N4 = N2 + N3

Therefore N5 = N3 + N4 and consequently

N6 = N4 + N5

Assuming this means that the missing number ,

N5 equals 233

However, it seems all too simple and I keep thinking that I have missed something Elementary , my dear Watson .

Sudi Sudarshan

Beginning with the third term, each number is the sum of the previous two numbers.

34+55=89

89+55=144

144+89=233

233+144=377

So, the missing number is 233.

Jose Padron

STAR ANSWER - Neat table

From Fibonacci sequence, the missing number is 233; where each number is the sum of the two preceding ones, starting with: 

And 0 and 1