10.8

Part of II Soros Olympiad 1995 - 96 (Russia)

Problems(2)

no from 1-100, Yes-No questions (II Soros Olympiad 1995-96 R1 10.8)

Source:

1

100

is intended. In what is the smallest number of questions one can surely guess the intended number, if one is allowed to lie once? (Questions are asked like: “Does the intended number belong to such and such a numerical set?” The only possible answers are “Yes” and “No.”)

combinatoricsnumber theory

1-,0,1 on nxn table (II Soros Olympiad 1997-98 R3 10.8)

Source:

Is it possible to fill an

n \times n

table with the numbers

-1

0

1

2n

sums in each column and each row are different? Solve the problem with a)

n = 5

n = 10