ERJ Brainteaser: November
22 Nov 2024
Q3 generated some particularly interesting replies, so it's congratulations to Amparo Botella, David Mann, Kamila Staszewska, Sudi Sudarshan, Andrew Knox, Michele Girardi and P J Swamy: new joint holders of the Brainiac of the Month title
Question 3: Six-pack
If 6 + 6 equals 14, what does 6 X 6 equal?
Answer: Well done to everyone who came up with the official answer 44 and to those who provided interesting, alternatives (see Solutions below): Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; David Mann, Polymer Business Development consultant, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; P J Swamy, managing director, Fores Elastomech India Pvt Ltd, Waluj, Aurangabad, Maharastra , India.
SOLUTIONS
David Mann
One possibility is that the puzzle is in base 8, so
One possibility is that the puzzle is in base 8, so
6 + 6 is 1 x 8 + 4.
In this system 6 x 6 would be
4 x 8 + 4 = 44.
Kamila Staszewska
It works when switched to octal system.
in decimal: 6+6=12
in octal: 12/8 = 1(quotient), 12-(8*1)=4(remainder), therefore it equals 14.
6x6=36 in decimal
36/8=4(quotient), 36-(8*4)=4(remainder), therefore in octal it equals 44.
Sudi Sudarshan
In the Base 8 system,
6 + 6 = 14 ( 1x8 + 4x1 = 12 = 6+6 in Base 10)
6 x 6 = 44 (4×8 + 4×1 = 36 = 6x6 in Base 10)
Michele Girardi
Trying numeric systems with bases other than 10 , 6+6 = 14 applies in base 8
6+6 = 12 = 1*8+*4*1
6x6 = 36 , that in base 8 is written 1004, since
36 = 1*32+0*16+0*8+4*1
Andrew Knox
If 6 + 6 equals 14, what does 6 X 6 equal?
Answer: 49
(6 clearly isn’t 6 here but 7)
Amparo Botella
I have two options:
- If we add one to each 6 the number will be:
7+7=14
7x7=49
- If we add 2 to the result we will have:
6-6=12+2=14
6x6=36+2=38
P J Swamy
Answer to Question 3 of November is : 49
Logic
Given 6+6 = 14
This can not be true as 6+6 in the mathematics we operate is 12.
However , if , as the question said , 6+6 = 14 , this 6 of this equation has to be 7 .
Then the 6x6 of the equation will in reality be 7x7 = 49
This is like if a man is a dog and how many men are there in two dogs ?
Question 2: Whatever next?
2,
1.73205…,
1.41421…,
?
Answer: Well done to everyone here who worked out that these numbers are the square roots of 4, 3, 2, in descending order, making 1 the correct answer: Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; John Bowen, consultant, Bromsgrove, UK; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan; David Mann, Polymer Business Development consultant, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Hans-Bernd Luechtefeld, consultant, Germany; Hans Eichenwald, marketing manager, durable labels, Label and Graphic Materials Europe, Oegstgeest, The Netherlands; P J Swamy, managing director, Fores Elastomech India Pvt Ltd, Waluj, Aurangabad, Maharastra , India; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA.
Question 1: Missing number
38, 11, 83
28, 10, 46
96, ?, 87
43, 7, 16
Answer: The official answer is 15, as so neatly worked out by this week’s highly select group: Hans-Bernd Luechtefeld, consultant, Germany; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; David Mann, Polymer Business Development consultant, UK; John Bowen, consultant, Bromsgrove, UK; PJ Swamy / P Srikanth, executive director, Fores Elastomech India Pvt Ltd, Waluj, Aurangabad, Maharastra, India; Andy Longdon, technical sales manager, Ceetak Ltd, Bedford UK; Special mention also to Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; who came up with an alternative, valid answer, taking a quite different approach.
SOLUTIONS
Hans-Bernd Luechtefeld
Dear all, the answer is 15. The number in the middle is the sum of the individual digits of the left and right numbers.
Andrew Knox
The answer is 15 ie the sum of the digits in the outer numbers is the middle number.
Michele Girardi
The missing number is 15 :
3+8 = 11 = 8+3
2+8 = 10 = 4+6
9+6 = 15 = 8+7
4+3 = 7 = 1+6
David Mann
Maybe I was overthinking this, the obvious answer is that the middle number is the sum of the digits of the left and right numbers, making the missing answer 15.
John Bowen
Missing number is 15 - In each case, the middle number is the sum of the digits of the number on each side.
PJ Swamy / P Srikanth
The answer is 15.
Logic
In each row, the middle number is the sum of the two digits of either the first number or the third number:
First row: the second number is sum of the digits of the first number 38 = 3+8= 11 or sum of the digits of the third number 83 = 8+3=11 . Therefore, the second number is 11.
Second row: the second number is sum of the digits of the first number 28 = 2+8= 10 or sum of the digits of the third number 46 = 4+6= 10. Therefore, the second number is 10.
Third row: the second number is sum of the digits of the first number 96 = 9+6= 15 or sum of the digits of the third number 87= 8+7= 15 . Therefore, the second number is 15 ie the missing number is 15.
Fourth row: the second number is sum of the digits of the first number 43= 4+3= 7 or sum of the digits of the third number 16= 1+6= 7. Therefore, the second number is 7.
Andy Longdon
Answer is 15:
3+8 = 11 = 8+3
2+8 = 10 = 4+6
9+6 = 15 = 8+7
4+3 = 7 = 1+6.
Kamila Staszewska
The answer is 6. The middle number in each line is the number to subtract from the number on the right and number on the left to make them divisible by 9:
38-11=27, 83-11=72
28-10=18, 46-10=36
96-6=90, 87-6=81
43-7=36, 16-7=9.
