<prompt> Kila moja ya dots tisa katika takwimu hii inapaswa kupakwa rangi nyekundu, nyeupe au bluu. Hakuna nukta mbili zilizounganishwa na sehemu bila vitone vingine kati zinaweza kuwa na rangi sawa. Je, kuna njia ngapi za kuchora dots za takwimu hii?asykuchora-75,0---45,0---60,26--mzunguko;kuchora0,0--30,0--15,26--mzunguko;chora75,0--105,0--90,26--mzunguko;chora-60,26--90,26;chora-45,0--75,0;nukta -75,0;nukta -45,0;nukta -60,26;nukta 15,26;nukta 0,0;nukta 30,0;nukta 90,26;nukta 75,0;nukta 105,0;asy  <response>: Kuna njia sita za kuchorea pembetatu ya equilateral upande wa kushoto. Bila upotezaji wa jumla, fikiria kuwa imepakwa rangi kama ilivyo hapo chini.asykuchora-75,0---45,0---60,26--mzunguko;kuchora0,0--30,0--15,26--mzunguko;chora75,0--105,0--90,26--mzunguko;chora-60,26--90,26;chora-45,0--75,0;nuktaB, -75,0, S;nuktaW, -45,0, S;nuktaR, -60,26, N;nukta 15,26;nukta 0,0;nukta 30,0;nukta 90,26;nukta 75,0;nukta 105,0;asyKisha kuna njia tatu za kuchorea pembetatu ya usawa wa kati:asyint i;transy jozi 0,-70;kwa i 0; i 2; i chorashiftitransy-75,0---45,0---60,26--cycle; kuchorakuhamaitransy0,0--30,0--15,26--mzunguko; chorashiftitransy75,0--105,0--90,26--cycle; chorashiftitransy-60,26--90,26; chorashiftitransy-45,0--75,0; nukta B, -75,0 itransy, S; nukta W, -45,0 itransy, S; nukta R, -60,26 itransy, N; nukta 15,26 itransy; nukta 0,0 itransy; nukta 30,0 itransy; nukta 90,26 itransy; nukta 75,0 itransy; nukta 105,0 itransy;nuktaB, 15,26, N;nukta R, 0,0, S;nukta W, 30,0, S;nukta W, 15,26 0,-70, N;nuktaR, 0,0 0,-70, S;nuktaB, 30,0 0,-70, S;nukta W, 15,26 0,-270, N;nuktaB, 0,0 0,-270, S;nuktaR, 30,0 0,-270, S;asySasa tunataka kupaka rangi pembetatu ya equilateral. Kwa kila kisa kilicho hapo juu, tuko katika nafasi sawa na hapo awali, kama wakati pembetatu ya kwanza ya usawa ilipotiwa rangi, na tulitaka kupaka rangi pembetatu ya pili ya usawa. Hii ina maana kwamba katika kila kesi, kuna njia tatu za rangi ya pembetatu ya equilateral ya tatu.Kwa hiyo, jumla ya idadi ya rangi zinazowezekana ni 6 cdot 3 cdot 3 54. 