 Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 553. (October 2017)

K. 553. A bag contains the numbers 1 to 200, written on cards. Andrew and Bill take turns drawing number cards one by one until the bag is empty. At the end, each of them adds his numbers together. Given that the first number drawn by Andrew is 3 and Bill's first number is 170, by what maximum amount may Andrew's sum exceed Bill's sum at the end?

(6 pont)

Deadline expired on November 10, 2017.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A lehető legnagyobb különbség András javára nyilván akkor lesz, ha Vili húzza az első 100 számot, kivéve a 3-at, ami helyett 170-et húzott, András pedig a többit:

 A 3 +101 +102 +103 ... +170 ... +200 -170 V 170 +1 +2 +3 ... +100 -3

Ha így írjuk fel a húzott számokat, akkor könnyű kivonni őket egymásból: $\displaystyle A – V = 3 – 170 + 100 · 100 – 170 – (-3) = 10 000 + 6 – 2 · 170 = 9666$.

### Statistics:

 209 students sent a solution. 6 points: 162 students. 5 points: 13 students. 4 points: 7 students. 3 points: 7 students. 2 points: 11 students. 1 point: 7 students. 0 point: 2 students.

Problems in Mathematics of KöMaL, October 2017