ERJ Brainteaser: November

Question 3: Table test II 

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