Question

Four friends ordered a pizza cut into eight slices. The whole pizza was eaten, with each friend eating a different number of slices. If no slice was divided, and no friend ate more than the other three put together, how many slices did each friend eat?

Answer 1

Answer:

{0,1,3,4}

Step-by-step explanation:

Given, total no of slices=8.

Total no of friends=4.

also each friend didnt ate more than the other three.

let a,b,c,d be no of slices ate by the friends 1,2,3,4 respectively.

given sum of a+b+c+d=8.

now applying the second condition

$a\leq b+c+d \\b\leq c+d+a\\c\leq a+b+d\\d\leq a+b+c$

so each of a,b,c,d must be less than or equal to 4.

which means 5 values are possible{0,1,2,3,4}.from this set you have to select 4 values such that their sum is 8.hence, those values are {0,1,3,4}.

Answer 2

Answer:

0,1,3,4

Step-by-step explanation:

Given each friend ate different number of slices and also slices are not divided

therefore assume w,x,y,z are the number of slices each friend got

w<x<y<z

z cannot be more than 4 as the no of remaining slices then will be less than 4

But its given no friend ate more than the other 3 put together

So by trial and error

z≤4,assume z=4

the y can ≤ 3

so possible outcomes (z=4,y=3,x=1,w=0)

x cannot be equal to one as the sum would exceed 8

this is the only possible outcome for z=4

for z=3

possible outcomes=(z=3,y=2,x=1,w=0) this is not possible as the sum is 6 but not 8

there is no use going less than z=3 as the sum would be lesser than 6

⇒ only one possible outcome z=4,y=3,x=1,w=0