ERJ Brainteaser: February
24 Feb 2025
For splendid use of pen & paper to resolve Q3, it's congratulations to Hans-Bernd Luechtefeld our new Brainiac of the Month
Question 3: Tough one?
14 36 ?
11 22 38
9.5 15 23
8.75 11.5 15.5
? 9.75 11.75
Answer: Not so tough after all, as neatly demonstrated (see Solutions below) by a select group of our top Brainiacs: Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; John Bowen, consultant, Bromsgrove, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; David Mann, Polymer Business Development consultant, UK; Hans-Bernd Luechtefeld, consultant, Germany; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA; Bharat B Sharma, technical director, Rajsha Chemicals Pvt. Ltd, (TWC Group), Vadodara (Guj) India. And, well done to everyone else who had a go.
SOLUTIONS
Kamila Staszewska
Given the middle column:
36-22 =14
22-15 = 7
15-11.5 = 3.5
11.5-9.75 =1.75
each number is reduced by half the previous amount.
Left column:
14-11=3
11-9.5=1.5
9.5-8.75=0.75
8.75-(0.75/2)=8.375
Right column, from the bottom:
15.5-11.75=3.75
23-15.5=7.5
38-23=15
38+(15*2) =68
The answer is 68 and 8.375.
John Bowen
The missing numbers are [LHS] 8.375 and [RHS] 68
As we go down the LHS we start by deducting 3 then successively half the deduction [1.5, 0.75 and so on]
On the RHS the deductions are 30, 15, 7.5 and so on.
The matrix now becomes:
14 36 68
11 22 38
9.5 15 23
8.75 11.5 15.5
8.375 9.75 11.75
Sudi Sudarshan
The missing numbers are 68 and 8.375.
Solution:
In each column, the difference between two consecutive numbers is double the difference between the next two number. Also the difference between numbers in the 1st and 2nd columns in each row is 11/16 the difference between numbers in the 2nd and 3rd columns.
Andrew Knox
The question mark at the top of the 3rd column is 68, at the bottom of column 1 is 8.375. Increments going from bottom to top of each of the three columns doubles in value.
David Mann
The differences between the numbers in the columns halve as they go down:
|
14 |
36 |
68 |
|
(3) |
(14) |
(30) |
|
11 |
22 |
38 |
|
(1.5) |
(7) |
(15) |
|
9.5 |
15 |
23 |
|
(0.75) |
(3.5) |
(7.5) |
|
8.75 |
11.5 |
15.5 |
|
(0.375) |
(1.75) |
(3.75) |
|
8.375 |
9.75 |
11.75 |
So, the missing numbers are 68 and 8.375.
Hans-Bernd Luechtefeld
(Splendid working-out in image above)
Amparo Botella
The missing numbers are 8,375 and 68
The numbers are got by adding minus a secunce, in the first sequence que have deducted 3 from de first number and then divided in half to deduct from next number, ie.. 3, 1,5, 0,75, 0,375. Same sequence in two next columns, and for the third on, as the next number to deduct is 15, we muzt add 30 to get the top number.
Peter Talbot
The difference between members of adjacent rows in the first column is halved as one goes down the table.
i.e. 14 – 11 = 3; 11-9.5 = 1.5; 9.5 – 8.75 = 0.75; therefore, the difference between column 1 row 4 and column 1 row 5 will be 0.375. Column 1 row 5 = 8.75 – 0.375 = 8.375.
The difference between members of column 3 and column 2 in the same row doubles as one proceeds up the table
i.e. 11.75 – 9.75 = 2 (row 5); 15.5 – 11.5 = 4 (row 4); 23 – 15 = 18 (row 3); 38 – 22 = 16 (row 2). The difference for row 1 will be 32, therefore Column 3 row 1 = 36 + 32 = 68
Bharat B Sharma
Question 2: Next number
What number comes next in this series?
100, 500, 1, 50, 1000, 5, ???
Answer: Well done to everyone who came up with the correct answer 10 (see Solutions below): David Mann, Polymer Business Development consultant, UK; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; John Bowen, consultant, Bromsgrove, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Hans-Bernd Luechtefeld, consultant, Germany; Bharat B Sharma, technical director, Rajsha Chemicals Pvt. Ltd, (TWC Group), Vadodara (Guj) India; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; and everyone else who had a go.
SOLUTIONS
David Mann
I think these are Roman numerals arranged in alphabetical order, so the next one will be 10 (X).
Amparo Botella
I think next number is 10
If we follow the series:
2nd, 4th. and 6th. number: 500 divided by 10=50 50 divided by 10=5
1st., 3rd. and 5th. number: 100 divided by 100=1 1 multiplied by 1000= 1000 the next one could be 1000 divided by 100=10
Kamila Staszewska
All numbers can be written as Roman numerals:
100, 500, 1, 50, 1000, 5
C, D, I, L, M, V
The last missing one is X = 10.
It also fits into alphabetical order.
John Bowen
Next number is 10
These are Roman numerals in alphabetical order:
C, D, I, L, M, V, then X or 10
Sudi Sudarshan
Solution: The Arabic numerals are in the alphabetical order of their Roman numeral equivalents.
100, 500, 1, 50, 1000, 5 translate to
C, D, I, L, M, V
The next letter of the alphabet used in the Roman Numeral System is X which translates to 10.
Hans-Bernd Luechtefeld
The numbers are all from Roman Numerals, when they are in order alphabetically:
C (100), D (500), I (1), L (50), M (1000), V (5) and then X (10).
Salvete omnibus
Bharat B Sharma
This is alphabetical series of roman numbers in ascending order.
Actually-
C (100),
D (500),
I (1),
L (50),
M (1000),
V (5) and then
X (10).
Andrew Knox
Answer: 10
These are the numerical equivalents of the Roman numerals listed in alphabetical order, i.e. C, D, I, L M V, X.
New teaser on Monday.
Question 1: Missing number
Answer: Well done to everyone who came up with the correct answer 106 and/or an interesting alternative answer 74 (see Solutions below): Kamila Staszewska, R&D / quality lead, Abcon Industrial Products Ltd, Cootehill, Co. Cavan, Ireland; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; John Bowen, consultant, Bromsgrove, UK; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Bharat B Sharma, technical director, Rajsha Chemicals Pvt. Ltd, (TWC Group), Vadodara (Guj) India; Tom Jenkins, business development, R.D. Abbott Co. Inc. Garden Grove, California, USA; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain.
SOLUTIONS
Kamila Staszewska
61=5*5+6*6
73=3*3+8*8
89=5*5+8*8
?=5*5+9*9=106
Andrew Knox
Answer: 106
(5^2 + 9^2)
In each “triplet”, the upper number is the sum of the squares of the two smaller numbers below.
John Bowen
Missing number is 106 - the top number is the sum of the squares of the lower two - ie 25 + 81 = 106
Sudi Sudarshan
The top number in each set of three numbers is the sum of the squares of the bottom two numbers.
(5^2)+(6^2) = 61
(3^2)+(8^2) = 73
(5^2)+(8^2) = 89
(5^2)+(9^2) = 25+81 = 106
Tom Jenkins
Sum of squares…
Bharat B Sharma
Numeratort is sum of squares of numbers in denominator.
Like
3x3 +8x8= 73
5x5+6x6 = 61
5x5+8x8 = 89
hence 5x5+9x9n=25+81=106.
Amparo Botella
The missing number is 74
Let’s start by the first two numbers 61 and 73, checking the sum of lower numbers:
5+6=11
3+8=11
61+11=72
That suggests we might need to add 12 instead of 11.
If we assume:
First number + sum of lower numbers+1= second number
Then:
61+(5+6)+1=61+11+1=73
Applying the same pattern for the missing number ? → 89:
Numbers below: (5,9) → (5,8)
Sum of first pair: 5+9=14
Sum of second pair: 5+8=13
Using the pattern:
?+14+1=89 ?+15=89 ? = 89 - 15 = 74
Using the pattern:
?+14+1=89 ?+15=89 ? = 89 - 15 = 74
Please note: Due to staff holidays, the next Brainteaser will be issued 17 February.
