Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 107. (December 2006)

K. 107. If two digits of the four-digit number 1234 are cancelled in every possible way and the remaining digits are read as a two-digit number, the numbers 12, 13, 14, 23, 24, 34 are obtained. Their sum is 120. Find a four-digit number for which this sum is a) 540; b) 220.

(6 pont)

Deadline expired on January 10, 2007.

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

Megoldás. a) pl. 9876. b) Nincs ilyen. Legyen a keresett négyjegyű szám alakú, ekkor a keresett összeg . Ez az összeg osztható 3-mal, a 220 pedig nem. Tehát az ilyen módon előállított számok összege nem lehet 220.

### Statistics:

 149 students sent a solution. 6 points: 95 students. 5 points: 7 students. 4 points: 12 students. 3 points: 33 students. 1 point: 1 student. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, December 2006