Photo:
THE MIRROR
A freight train transports ore from the port of Hamburg to a steel works in Salzgitter.
The 40 wagons together weigh 5700 tons.
They are of different weight.
However, we know that three wagons hanging one behind the other always weigh exactly 430 tons.
What is the combined weight of the middle two wagons?
320 tons.
If the first three cars have the
masses a, b
and
c
, the fourth car must again have the mass a so that the mass of three consecutive cars does not change.
Wagon 5 therefore has mass b, wagon 6 has mass c and wagon 7 starts again with mass a.
The masses a, b, c follow one another again and again in this order – namely 13 times up to wagon 39. The first 39 wagons therefore weigh 13*430 = 5590 tons.
Wagon 40 again has the mass a.
Because the train weighs a total of 5700 tons,
a = 5700 - 5590 tons
a = 110 tons and
b + c = 430 tons - a
b + c = 320 tons.
The cars in the middle have the numbers 20 and 21. They therefore have the masses b and c.
Therefore 320 tons is the solution we are looking for.
I discovered this puzzle in the puzzle collection "Math with the Kangaroo 2019" of the student competition of the same name.
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