ERJ Brainteaser: February
7 Feb 2025

Each month, ERJ sets a weekly brainteaser, with questions of varying degrees of difficulty. Readers supplying the most accurate (and stylish) answers are then considered for the prestigious Brainiac of the Month title.
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.