We have a clear, standout 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, ChemTrend 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, ChemTrend 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 mathstake 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 = 91 =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