# 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.