Baltic Way 1993 · Problem 15

Combinatorics

On each face of two dice some positive integer is written. The two dice are thrown and the numbers on the top faces are added. Determine whether one can select the integers on the faces so that the possible sums are $2,3,4,5,6,7,8,9,10,11,12,13$ , all equally likely?

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Review

Topics

Counting and enumeration

Solutions

Solution

Solution:

We can write $1, 2, 3, 4, 5, 6$ on the sides of one die and $1, 1, 1, 7, 7, 7$ on the sides of the other. Then each of the 12 possible sums appears in exactly 3 cases.

Contest context

Results from Baltic Way 1993

8 teams

Mean score: 4.9 / 5
Scores of 4 or 5: 8 / 8
Estonia: 4 / 5

Score distribution

All team scores

Team	Score
Poland	5 / 5
Latvia	5 / 5
Estonia	4 / 5
Sweden	5 / 5
Lithuania	5 / 5
Finland	5 / 5
Iceland	5 / 5
Denmark	5 / 5

Elsewhere

AoPS · Baltic Way 1993
Official results