### Brain Teasers

# Madadian Cricket

Smelly O'Riley, Drooling David and Gangly Gordon played in a Cricket match between Madadia and England.

None of them scored more than 99 runs.

If you add the digits of the runs scored by Smelly to his own score, you will get the runs scored by David.

If you reverse the digits of the runs scored by David, you will get the runs scored by Gangly.

The total runs scored by them is 240.

Can you figure out their individual scores?

None of them scored more than 99 runs.

If you add the digits of the runs scored by Smelly to his own score, you will get the runs scored by David.

If you reverse the digits of the runs scored by David, you will get the runs scored by Gangly.

The total runs scored by them is 240.

Can you figure out their individual scores?

### Answer

Smelly, David and Gangly scored 75, 87 and 78 respectively.Smelly's score must be less than 86, otherwise David's score would be more than 99. Also, he must have scored at least 42 - in case David and Gangly scored 99 each.

Also, as none of them scored more than 99 and the total runs scored by them is 240; their individual scores must be around 80.

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## Comments

OK! You got the answer from a book so you want me to explain it! I really like this one. It is a Diophantine equation with a twist.

If you let Smelly score x+10y then clearly David scores 11y+2x after adding the digits. Heres the twist. Which parts of Davids is the tens column and which part is the units column?CASE1 10y + (y+2x)

CASE2: If when we added Smelly's digits there was a carry digit then it is broken up 10(y+1) + (y+2x-10) I tried the second case first because it is sneakier. Adding all of their scores and rearranging the equation to make x the subject gives x=(339-32y)/23. A bit of trial and error (You don't have to do every calculation because it falls into a pattern) gives x=7 , y=5. Hence Mad-Ades answer!

Got any more like that?

If you let Smelly score x+10y then clearly David scores 11y+2x after adding the digits. Heres the twist. Which parts of Davids is the tens column and which part is the units column?CASE1 10y + (y+2x)

CASE2: If when we added Smelly's digits there was a carry digit then it is broken up 10(y+1) + (y+2x-10) I tried the second case first because it is sneakier. Adding all of their scores and rearranging the equation to make x the subject gives x=(339-32y)/23. A bit of trial and error (You don't have to do every calculation because it falls into a pattern) gives x=7 , y=5. Hence Mad-Ades answer!

Got any more like that?

Um, aside from the math and all, is it true that a cricket game can go on for days? And if so, did that contribute to the fall of the British empire? The soldiers could have been very caught up in criket...

I cannot believe anyone would make such an absurd comment thinking it was funny.

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