ERJ Brainteaser: October
27 Oct 2023
For the first time ever, the Brainiac of the Month title goes to the ERJ question-setter for stumping even our most expert readers with Q3...
Question 4: Give me five
Complete the five-number sequence, starting:
1, 10, 11…
Answer: We are looking here* at binary numbers 1 to 5, so it’s: 1, 10, 11, 100, 101. Well done to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; David Mann, key account manager, SPC Rubber Compounding, UK; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Jose Padron, laboratory analyst, Toyoda Gosei WTG, Quebec, Canada; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA.
*There was also a valid solution – 1, 10, 11, 21, 32 with each number being the sum of the previous two – from Andrew Knox and John Bowen, consultant, Bromsgrove, UK.
Question 3: Top table
3 |
7 |
11 |
12 |
0 |
6 |
22 |
19 |
20 |
1 |
3 |
13 |
? |
20 |
9 |
2 |
17 |
5 |
4 |
6 |
4 |
13 |
17 |
18 |
8 |
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:
X |
* |
Y |
-1 |
= |
X |
10 |
* |
1 |
-1 |
= |
9 |
9 |
* |
2 |
-1 |
= |
17 |
17 |
* |
3 |
-1 |
= |
50 |
50 |
* |
4 |
-1 |
= |
199 |
199 |
* |
5 |
-1 |
= |
994 |
994 |
* |
6 |
-1 |
= |
5963 |
5963 |
* |
7 |
-1 |
= |
41740 |
And so on…