This year's wits games tournament was very disputed. The first four classified were four participants from the same country:

- Idi Amin solved more riddles than Idi Bamin.
- Between the two, Idi Camín and Idi Damín, they solved as many as Idi Amín and Idi Bamín.
- Idi Camín and Idi Amín resolved less than Idi Bamín and Idi Damín.

**In what order were the four classified?**

#### Solution

If we assume that

A: are the riddles solved by Idi Amí-n.

B: are the riddles solved by Idi Bamí-n.

C: are the riddles solved by Idi Camí-n.

D: they are the riddles solved by Idi Damí-n.

From the first statement we have to:

A> B

Of the second:

C + D = A + B ⇒ D - A = B - C **(Equation 1)**

From the third:

A + C ** C - B (Equation 2)**

**Substituting the equation (1) in (2):**

B - C> C - B ⇒ 2B> 2C => B> C

**As B> C we can deduce that:D - A = B - C> 0 ⇒ D - A> 0 = D> A**

**Therefore the order of classification was as follows: 1st: Idi Damí-n, 2nd: Idi Amí-n, 3rd: Idi Bamí-n and 4th: Idi Camí-n**