ERJ Brainteaser: November
24 Nov 2023
We have a clear, stand-out winner this month, not least for answering Q4. Congratulations to David Mann of SPC Rubber Compounding, our new Brainiac of the Month.
Question 4: Prime puzzle?
10 + 9 = 52
8 + 7 = 36
6 = 5 = 24
4 + 3 = 12
2 = 1 = ?
Answer: Many attempts, but there was only one codebreaker: extremely well done to David Mann, key account manager, SPC Rubber Compounding, UK:
If you read 10 + 9 as 10th prime number + 9th prime number etc., then:
> 10 + 9 = 23 + 29 = 52
> 8 + 7 = 19 + 17 = 36
> 6 + 5 = 13 + 11 = 24
> 4 + 3 = 7 + 5 = 12
> 2 + 1 = 3 + 2 = 5
New teaser on Monday.
Question 3: Table test II
6 |
7 |
4 |
2 |
6 |
8 |
5 |
4 |
7 |
6 |
4 |
1 |
8 |
8 |
7 |
6 |
9 |
7 |
? |
? |
Answer: Not sure why this happens so often but yet again there is more than one valid answer to our teaser. The official answer is 7 and 5 (as per David Mann’s solution below). But, perhaps unsurprisingly, other Brainiacs came up with an alternative solution.
So, it's very well done to: David Mann, key account manager, SPC Rubber Compounding, UK; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and everyone else who had a go.
SOLUTIONS
David Mann
One solution as follows:
Add the numbers in columns 1 and 2. Then sum the digits and put the result in column 3. Add columns 2 and 3 together, then sum the digits of that result. So the missing numbers are 7 and 5.
Michele Girardi
Hi everybody, the missing cells could be 16 and 23.
There are two coincidences:
- the sum of the first two columns is 36, the numbers that make the sums of the third and the fourth columns equal to 36 are 16 and 23.
- the third column is the average of the first and the fourth, and this is respected also using the numbers above
John Bowen
Missing numbers are 16 and 23 [each of columns 1 and 2 add up to 36 ; to make columns 3 and 4 do likewise the above numbers are required]
Andrew Knox
Answer: Bottom row is 9, 7, 16, 23.
(Each column then adds up to 36).
Question 2: Number cruncher V
12, 36, 324, 2916, 52488, ?...
Answer: Each number is multiplied by the sum of its digits, making the next number 1,417,176, as per Solutions (with some interesting notes) below. Well done to: John Bowen, consultant, Bromsgrove, UK; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; Ian Brooker, buyer, HB Chemical Corp., a Ravago Company, Twinsburg, Ohio, USA; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA; 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; and everyone else who had a go.
SOLUTIONS
John Bowen
Sum of digits of first number is=3+6=9
So, next digit will be=36*9=324
Sum of digits of 324=3+2+4=9
So, next digit will be=324*9=2916
Sum of digits of 2916=2+9+1+6=18
So, next digit will be=2916*18=52488
Sum of digits of 52488=5+2+4+8+8=27
So, next digit will be=52488*27=1417176
Stephan Paischer
The figure is multiplied with the sum of its digits (for 52488, this is 27 – so 52488 x 27 = 1417176).
Peter Talbot (and wife)
1,417,176 is the answer.
Sum the digits of each number and multiply that number by the sum to make the succeeding number.
Examples: using 12. 1+2 = 3; 12 X 3 = 36; using 36, 3+6 = 9; 36 X 9 = 324; using 324, 3+2+4 = 9; 324 X 9 = 2916.
Using 2916, 2+9+1+6 = 18; 2916 X 18 = 52488; using 52488, 5+2+4+8+8 = 27; 52488 X 27 = 1,417,176
Andrew Knox
(Sum of individual digits times the number itself forms the next number, so 1+2 = 3, times 12 = next number 36).
This sequence was especially frustrating as the sequence ALMOST fits a number of other, more logical mathematical sequences, such as:
2 squared x 3 = 12,
2 squared x 3 squared = 36,
up to 2916 = 2 squared x 3 to the power 6,
or
12 squared/4 = 36,
36 squared/4 = 324,
324 squared/4 = 26244 (not good, but a number that appears later in the sequence.... and if then divided by 9, = 2916,
or
12 = 2 squared x 3
36 = 6 squared
324 = 18 squared
2916 = 54 squared
52488 = 162 squared x 2, whereby 2 x 3 = 6, 6 x 3 = 18, 18x 3 = 54, 54 x 3 = 162....
David Mann
In this sequence the term is multiplied by the sum of its digits.
The next term will be:
52488 x (5 + 2 + 4 + 8 + 8) = 52488 x 27 = 1417176
Michele Girardi
the next number is 1417176, each one is equal to the previous multiplied its sum of digits:
12 2^2*3
12*(1+2) = 36 = 2^2*3^2
36*(3+6) = 324 = 2^2*3^4
324*(3+2+4) = 2916 = 2^2*3^6
2916*(2+9+1+6) = 52488 = 2^3*3^8
52488*(5+2+4+8+8) = 1417176 = 2^3*3^11
Despite the method of formation of the numbers, they are all factorizable as powers of 2 and 3, with a sequence of exponents not clearly defined.
Question 1: Country counter
Austria + USA = 9
Malaysia + Puerto Rico = 10
Malaysia + USA = ?
Answer: The key was to recognise that the figures referred to the number of red stripes on the flags of these various countries, making the answer:
Austria (2) + USA (7) = 9
Malaysia (7) + Puerto Rico (3) = 10
Malaysia (7) + USA (7) = 14
Setting the standard were: David Mann, key account manager, SPC Rubber Compounding, UK; and Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands: sending in the correct answer early on Monday, well before any clues were issued. They were followed soon after by: Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria; Sudi Sudarshan, strategic market & technology insights lead, Bridgestone Americas Inc. USA; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy. Well done to all, and everyone else who had a go.
Another solution
Extra special mention to Michele Girardi for this clever maths-take on the question:
Let's consider the number of vowels
Austria 4
USA 2
Malaysia 4
Puerto Rico 4
And look for coefficients a,b to multiply the number of vowels
a*4+b*2 = 9
a*4+b*4 = 10
It's b*2 = 1 b= 1/2
a*4 = 9-1 =8 a=2
Verification :
Austria + USA = 2*8+1/2*2 = 9
Malaysia + Puerto Rico = 2*4 + 1/2*4 = 10
applying to the 3rd expression
Malaysia + USA = 2*4+1/2*2 = 9