ERJ Brainteaser: March
28 Mar 2024
For their answers to Q1 and Q3 respectively, it’s congratulations to Ian Brooker, HB Chemical and Jose Padron, Toyoda Gosei, new joint holders of the Brainiac of the Month title
Question 4: Food fight
Chef Gordon ordered 2kg of potatoes and 3kg of onions, while rival chef Alain ordered 1kg of potatoes and 1kg of onions. If 1kg of potatoes costs €2.30 more than 1kg of onions and Alain paid a total of €4.20 for his order, what was Gordon’s bill?
Answer: Okay, not much of a ‘fight’ and it seems both chefs are paying a bit over the odds for their vegetables. Anyway, very well done – in order of reply – to these readers, who neatly worked out Gordon’s bill at €9.35: John Bowen, rubber & tire industry consultant, Bromsgrove, UK; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain; Antonella Pagliarulo, product development manager, Performance Polymer Solutions, Thomas Swan & Co. Ltd, Consett, County Durham, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, quality manager, Scame Mastaf SpA, Suisio, Italy; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Peter D. Talbot, research scientist, Chem-Trend LP, Howell, Michigan, USA; Jose Padron, laboratory analyst, Toyoda Gosei, Waterville, QC, Canada; and everyone else who had a go.
SOLUTIONS
John Bowen
Gordon = G, Alain = A, price of potatos#es = P, and of onions = O
G = 2P + 3O [1]
A = P + O [2]
and P = O + 2.3 [3]
We know P + O = 4.2 [4]
Substitute for P:
2O + 2.3 = 4.2
So 2O = 1.9, thus O = £0.95/kg
Substitute in [4], P = £3.25/kg
and in [1], G = £6.5 + £2.85 = £9.35
Amparo Botella
X+(x+2,30)=4,20
2x=4,20-2,30
X=1,90/2=0,95
The price of the Potatoes is 3,25 and the onions is 0,95
Chef Gordon spent = 9,35 (3x0,95)+(2*x3.25)
Antonella Pagliarulo
If the cost of onions is x €/kg, then the cost of potatoes is 2.30+x €/kg.
Alain’s bill: (2.30+x) + x = 4.20
Gordon’s bill: 2(2.30+x) +3x = y
Solving these equations gives:
cost of onions x = 0.95 €/kg
Gordon’s bill y = €9.35
Andrew Knox
If onions cost X/kg, then potatoes cost X + 2,30/kg
Solving for X: 2X +2,30 = 4,20, giving X = EUR 0,95, Gordon's bill is then 5X + 4,60 = EUR9,35
Arkanath Sudarshan
Let P = Price per kg of Potato
O = Price per kg of Onion
Gordon's total cost = 2P+3O
Alain's total cost = P+O = 4.20
P = O+2.30
P - O = 2.30
P + O = 4.20
Adding the two equations: 2P = 6.50 or P = 3.25
Substituting for P, 3.25 = O = 2.30 or O = 0.95
Chef Gordon's bill = 2*3.25 + 3*0.95 = 6.50 + 2.85 = €9.35
Michele Girardi
Gordon's bill was 9.35€.
Expressing the problem in equations :
G = 2*p + 3*o
A = p + o = 4.2
p - o = 2.3
Summing the 2nd and the 3rd
2*p = 4.2 + 2.3 = 6.5
subtracting
2*o = 4.2 - 2.3 = 1.9
3*o = 3/2*1.9 = 2.85
G = 2*p + 3*o = 6.5 + 2.85 = 9.35
Jose Padron
From Gordon:
2P + 3O = X
From Alain:
P + O = 4.20
Where; P = potatoes and O = onions
Additionally; P = O + 2.3
Solving O in Alain’s
(0+2.3) + O = 4.20
2*O = 4.2 – 2.3
O = 1.9/2 = 0.95
Solving P in Alain’s
P + 0.95 = 4.20
P = 4.20 – 0.95 = 3.25
Thus, from Gordon’s
2*3.25 + 3*0.95 = X
6.50 + 2.85 = 9.35
So, the result; Gordon’s bill is €9.35
Peter D Talbot
P = potato, O = onion.
Alain: P + O = €4.20, P = O + €2.30
Gordon: 2O + €2.30 = €4.20, 2O = €1.90, O = €0.95
P = €0.95 + €2.30 = €3.25
Gordan’s bill was for 2kg potatoes (€6.50) + 3kg onions (€2.85) = €9.35.
Due to the Easter holidays, the next Brainteaser - and ERJ Daily Newsletter - will be issued on Tuesday.
Question 3: Odd days
In some parts, the term ‘odd days’ is used for dates which can be written as a sequence of consecutive odd numbers.
One such number, for example, is the ninth of November 2013, which can be written 9/11/13.
How many other ‘odd dates’ occur this century?
Answer: Not our usual type of question, but this teaser did generate a set of neat replies (see Solutions below). Nicely done to: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Jose Padron, laboratory analyst, Toyoda Gosei WTG, Quebec, Canada; and everyone else who had a go.
SOLUTIONS
Andrew Knox
Answer: 4 (01/03/05, 03/05/07, 05/07/09, 07/09/11). There are five in total, but the question specifically asks for "other" than 9/11/13.
One could argue that there are a further 5 correct dates if a reversed sequence is permitted (13/11/09, 11/09/07, 09/07/05, 07/05/03, and 05/03/01). In which case the answer is 9. Or 10.
Sudi Sudarshan
My Answer: 4
Solution: assuming leading zeroes are ignored,
01/03/05, 03/05/07, 07/09/11, 09/11/13, 11/13/15
Jose Padron
Let’s take the next considerations:
- Century (XXI) starting in 2001 to 2100.
- All even years are eliminated; 2002, 2004… 2098, 2100.
- All even months are eliminated; February, April, June, August, October and December.
- All even days are eliminated; 2, 4, 6… 28, 30.
- both 2001 and 2003 years are eliminated on both UK and US style, because no combinations are possible in these years.
- three calendar styles; UK, US and Canadian English.
Thus; results are:
- Five odd days for the UK style calendar.
- Six odd days for the US style calendar.
- Five odd days for the Canadian English style calendar.
Question 2: Crossways challenge
Answer: For a second week in a row our teaser proved a bit more challenging than usual. The key was to recognise that by multiplying the central number with the top number and then adding the bottom number you got the three-digit centre number. So as 8 X 14 = 112, you need to add 76 to get 188. Extra well done to Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Stephan Paischer, head of product management and market intelligence, Semperit AG Holding, Vienna, Austria, and everyone else who had a go.
Question 1: First and four-most
If FOURTH = 12 and THIRD = 9, what does FIRST equal?
Clues: SECOND is also equal to 9, F = 4..., I = 1....
Answer: Hats off to Ian Brooker, senior buyer, HB Chemical Corp., a Ravago Company, Twinsburg, Ohio, USA – the only reader to come up with correct answer 8 for this tricky Scrabble-based teaser.
