watch probably)

While the salesmen isn?t watching, the buyer turns the price upside down and gets the car for 1626

less. How much did the car initially cost

 

 

I guess there is a super-smart solution for this, but if you want a way to go about solving here is one:

 First recognise the possible digits: 0,1,2,5,6,8,9.

 

Next a table of how do the digits look on inversion

 

Col 1      Col 2

0              0

1              1

2              2

5              5

6              9

8              8

9              6

 

So now, a number a₁b₁c₁d₁ got transformed to d₂c₂b₂a₂ where 1 is Col1 and 2 is Col 2 i.e. a₁ gets inverted into a₂ and moves to the units place etc.

 

Sinc the difference is 1626, we must have a₁-d₂ = 1 or 2 and d₁-a₂ = 6 or a₂-d₁ = 4.

From the possible pairs we get a₁ = 6; a₂ = 9; d₁ =d₂ = 5.

 

So we move to the middle two digits.

Method I :Since, 1 gets carried from c₁, we c₁-b₂ = 3 or b₂-c₁ = 7.

We must simultaneously have b₁-c₂ = 6 or b₁-c₂ = 7 (as 1 does not get subtracted from the last digit)

 

This is satisfied by b₁ = 8 and c₁=1.

 

Method 2: Since 1 gets carried from c₁ and 1 is not subtracted from a₁, b₁c₁ - c₂b₁ = 63. Hence, b₁ = 8 and c₁=1.

 

Hence the cost was Euro 6,815 which the customer got for Euro 5,189

 

Euro because the sale took place in Belgium

 

This may be the Flanders which is a bit easier.