Abstract
The texts and solutions of the Lithuanian school mathematical olympiad-2009 are presented.
Highlights
Juozas Juvencijus MAC YSJei b = 2, tai 14a = 44, sprendiniu nera.
Kad b turi dalytis iš 7, todel b 7, bet tada 30b 210, ir sprendiniu nera.
Jei visu šešiu prietaisu rodmenu suma yra lygi 7?.
Summary
Jei b = 2, tai 14a = 44, sprendiniu nera. Kad b turi dalytis iš 7, todel b 7, bet tada 30b 210, ir sprendiniu nera. Jei visu šešiu prietaisu rodmenu suma yra lygi 7?. Jei M sutampa su O, tai M yra lygiai už 3 metru nuo visu šešiakampio viršuniu, ir taške M mieganti mokini matytu visi 6 prietaisai. Jei M nesutampa su O, tai taško M atstumai nuo A ir B ne didesni už 3: ABM kampai A ir B ne didesni už 60◦, kampas M 60◦, todel AM AB, BM AB. Jeigu tokiu mokiniu atitinkamai yra a, b ir c, tai bendras rodmenu skaicius lygus 2a + 3b + 6c = 7. 4. Naturaluji skaiciu N vadinkime paslankiuoju, jeigu ji galima užrašyti keliu (nebutinai skirtingu) naturaliuju skaiciu suma taip, kad visu demenims atvirkštiniu skaiciu suma butu lygi 1.
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