# The ingenuity tournament 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