Boris chooses 3 different numbers. The sum of the 3 numbers is 36. One of the numbers is a cube number. The other 2 numbers are factors of 20. Find the numbers that Boris has chosen.

The numbers are 27, 4 and 5

Numbers are 27, 5, 4.

Step-by-step explanation:

Boris chooses 3 different numbers.

Sum of first 3 numbers is 36.

One of the 3 numbers is a cube number.

That number may be 1³ = 1 or 2³ = 8 or 3³ = 27

[Not more than 4³ because 4³ = 64 and sum of the three numbers is 36 which less than 64]

It is given that other 2 numbers are the factors of 20. So the numbers may be either 10 and 2 or 5 and 4.

So sum of these numbers should be either 5+4 = 9 or 10+2 = 12.

a). If third number is 1 then sum of other two numbers will be 35 but it is not true, because sum of these two numbers should be either 9 or 12.

b). If the third number is 8 then sum of other two numbers will be 28 but it is not true, because sum of these two numbers should be either 9 or 12.

c). If the third number is 27 then the sum of other two numbers will be (36 - 27 = 9).

Therefore, the numbers are 27, 5, 4.