1. Cricket Match

In a cricket match, one team made 315 runs, all which are made by batsmen. If all eleven batsmen have made different runs and the batsmen who made maximum runs has made 32 runs then at least how many runs must be made by the batsmen who made the minimum runs?

2. Hello, magentarita!

Is there a typo?
The facts do not add up . . .

In a cricket match, one team made 315 runs, all which are made by batsmen.
If all eleven batsmen have made different runs
then at least how many runs must be made by the batsmen who made minimum runs?
Consider the top ten batsmen.
They have 10 different scores with a maximum of 32.

The most they could have is: . $23 + 24 + 25 + \hdots + 32 \:=\:275$

This leaves: . $315 - 275 \:=\:40$ for the eleventh batsman,
. . which is clearly impossible.

3. maybe...

Originally Posted by Soroban
Hello, magentarita!

Is there a typo?
The facts do not add up . . .

Consider the top ten batsmen.
They have 10 different scores with a maximum of 32.

The most they could have is: . $23 + 24 + 25 + \hdots + 32 \:=\:275$

This leaves: . $315 - 275 \:=\:40$ for the eleventh batsman,
. . which is clearly impossible.
Maybe there is a typo. I'll get back to you. What did you do on your memorial weekend?