ERJ Brainteaser: October

Question 3: Top table

Answer: With a little help (clue: '7 + 11 + 12 =') our teaser was finally solved (see Solutions below), Well done to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; David Mann, key account manager, SPC Rubber Compounding, UK; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; John Coleman, membership manager, Circol ELT, Dublin, Ireland; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA.

SOLUTIONS

David Mann

Thanks to the clue, the outer columns show the digits of the three centre columns.

So, the missing number is 6 (13 + 6 + 20 = 39)

Good one!

Michele Girardi

The answer is 6: the sum of the central values is equal to the number obtained coupling the first and the fifth:

7+11+12 = 30

22+19+20 = 61

13+6+20 = 39

17+5+4 = 26

13+17+18 = 48

There's some learning on that, the solution could be found by regression, but it didn't work because I specified the model with constant.

Without constant it's easily found 

x3 = 10,00 x1 - 1,000 x2 - 1,000 x4 + 1,000 x5

x2+x3+x4 = 10x1+x5

Sudi Sudarshan

Thanks to your clue: I was able to figure this out!

The sum of the middle three numbers in each row is the concatenation of the first and last numbers in that row.

7+11+12 = 30

22+19+20=61

17+5+4 = 26

13+17+18 = 48

13+?+20 = 39

? = 6

John Coleman

By following the clue available we can deduce that joining column 1 and column 5 together equates to the sum of columns 2, 3 & 4.

Therefore, 3 & 9 = 39 = 13 + ? + 20.

This means that ? = 39-13-20 = 6.

That was a good one!

Peter D. Talbot

The answer is 6 (how did I not see that?)!

The sum of the inside 3 numbers of each row equals the number represented by the outside members of the same row (1st column “tens”, 5th column “ units” in olde English terms.

Your clue made this infuriating puzzle look very simple in the end, thanks.

Question 2: Where next?

Egypt (20%), Italy (40%), Kasakhstan (30%), Italy (40%), _?_ (50%), India (60%).

Email your answer; correct replies on Friday*.

Answer: There is a surprisingly large number of countries that meet the criteria here, ie having a 50% ratio of vowels to consonants in their name. Readers identified Azerbaijan, Cambodia, Canada, Greece, Mozambique, Mexico and Taiwan, among many others. Well done to: John Coleman, membership manager, Circol ELT, Dublin, Ireland; David Mann, key account manager, SPC Rubber Compounding, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; and everyone else who had a go.

Solutions

Some select replies:

John Coleman

O man, that’s a toughie…

Oman (50%) - Ratio of vowels to consonants.

Sudi Sudarshan

I have two possible answers for this week’s brainteaser: Azerbaijan and Mozambique.

The country names alternate in length between 5 and 10 letters. So the missing name has 10 letters.

The percentage refers to the percent of vowels in the names:

Egypt – 1 vowel out of 5 = 20%

Kasakhstan – 3 vowels out of 10 = 30%

Italy – 2 vowels out of 5 = 40%

India – 3 vowels out of 6 = 60%

Azerbaijan - 5 vowels of of 10 = 50%

Mozambique – 5 vowels out of 10 = 50%

Egypt is in Africa, Kazakhstan in Asia, Italy in Europe. If we assume a repeat cycle of the continents, the next one would be from Africa, followed by Asia (India). So my selection is Mozambique!

Michele Girardi

Hello everybody,

The answer could be Belgium, Greece  or Mexico, and all  country names where the number of vowels is 50% of the letters. [But ]IMHO the question is imperfect, since y can be considered a vowel depending on its position in the word, which is the case for Egypt but also for Italy, so Italy should be 60%.

Question 1: A fine sequence

Find the next number in the following sequence: 10, 9, 17, 50, 199, _

Answer: Easy if/when you know how: the answer is 994 (see Solutions below) as neatly worked out by: John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; Peter D. Talbot, Research Scientist, Chem-Trend LP, Howell, Michigan, USA; David Mann, key account manager, SPC Rubber Compounding, UK; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada. Well done to all, and everyone else who had a go.

SOLUTIONS

John Bowen

10 x 1-1= 9

9 x 2-1= 17

17 x 3-1= 50

50 x 4-1= 199

199 x 5-1= 994

Andrew Knox

Sequence is x 1, 2, 3, etc. Minus 1 = next number.

10x1-1= 9

9x2-1= 17

17x3-1= 50

50x4-1= 199

199x5-1=994

Michele Girardi

Every number is obtained by mutiplying the previous  for the progressive number and subtracting 1 or

N(i) = N(i-1)*(i-1)

i N(i)

1         10

2         9      = 10*1-1

3         17    = 9*2-1

4         50     =  17*3-1

5         199   =    50*4-1

6         994   =   199*5-1

Sudi Sudarshan

Solution:

nth number = ((n-1)th number)*(n-1) - 1

10

10*1-1= 9

9*2-1= 17

17*3-1= 50

50*4-1= 199

199*5-1= 994

Peter D. Talbot

(10 x 1) – 1 = 9; (9 x 2) – 1 = 17; (17 x 3) – 1 = 50; (50 x 4) – 1 = 199; (199 x 5) – 1 = 994

David Mann

Take the first term, multiply by 1, subtract 1.

Then take the result, multiply by 2, subtract 1, and so on.

The next term will be (199x5) -1 = 994

Jose Padron

Considering the following repeating sequence:

X =(X*Y)-1

Starting with X = 10 and taking the result as the next X-value and, Y will be incrementing by one: Y = Y+1 each iteration.

Here is a table to show how this sequence works:

And so on…