Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 91. (October 2006)

K. 91. 2163 is a four-digit number in which the digit in the units' place is three times the digit in the hundreds' place, and the digit in the tens' place is two times the sum of the digits in the hundreds' place and the thousands' place. Is it true that such four-digit numbers are all divisible by 3?

(6 pont)

Deadline expired on November 10, 2006.

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

Megoldás. Igen. A keresett négyjegyű számok számjegyei balról jobbra haladva: a, b, 2a+2b, 3b, ezek összege 3a+6b, ami osztható 3-mal, tehát a megfelelő tulajdonságú négyjegyű számok is oszthatók 3-mal.

### Statistics:

 262 students sent a solution. 6 points: 112 students. 5 points: 45 students. 4 points: 28 students. 3 points: 24 students. 2 points: 25 students. 1 point: 17 students. 0 point: 8 students. Unfair, not evaluated: 3 solutions.

Problems in Mathematics of KöMaL, October 2006