Math game #2

difficulty level: 5th grade

Johnny found 6 natural numbers that their sum is 2019, and he has spoiled 3rd largest number to Mary. Mary could find all the other numbers after it so what number Johnny did tell to Mary?

answer with explanation

gets 10 akorns

edit: i forgot to say all 6 numbers are different

Quote from 4NIA4

Six numbers in sequence that adds up to 2019.

The average number of six numbers.

2019/6 = 336.5

Trying number +/- 3 on this number are. 333 - 338.

333 + 334 + 335 + 336 + 337 + 338 = 2013

Total is 6 less than 2019. Shifting the number set up 2, 335 - 340.

335 + 336 + 337 + 338 + 339 + 340 = 2025

Total is 6 too much. Shifting number set down 1, 334 - 339.

334 + 335 + 336 + 337 + 338 + 339 = 2019

337

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numbers can have difference more than 1

for example if Mary gets 337

it can be 240,317, 322,337,400,403

sum is 2019 and 337 is third largest like this there are so many possibilities

but the number Johnny tells has only one possibility so no

4NIA4 u think numbers should be in sequence if that's the case it is easy tho

x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=2019

6x+15=2019

6x=2004

x=334

then x+3=334=3=337 can be found easily

but number don't have to be in sequence duh

Quote from autumnleaf_soshi

is the answer 671?

that is the highest it can go for the 3rd number

1+1+1+671+672+673=2019

Since it says there are two more upper number that are greater and it's also saying the 3rd largest meaning the 2nd and the largest number must have a difference between them.

So the 3rd largest number cannot be more than 671 so Johnny must have said 671 or else there are multiple solutions Mary can make up for herself. But if the number is 671 then Mary is stuck with 1+1+1+671+672+673=2019

Mary has no way of changing any other number if the 3rd number is 671

I don't know man this is all I got.

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sorry i have forgot to say that all numbers are different

u have written the first three numbers all 1 but okay i am gonna consider this