ꯈꯉꯅꯗꯕ ꯔꯨꯂꯦꯠ ꯆꯛꯔꯁꯤꯡ

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫

1. ꯑꯣꯁ꯭ꯇ꯭ꯔꯦꯂꯤꯌꯥꯗ ꯁꯦꯃꯈꯤꯕ ꯔꯣꯌꯦꯜ ꯔꯨꯂꯦꯠꯇ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 50 ꯂꯩ: 2 ꯗꯒꯤ ꯀꯤꯡ ꯐꯥꯑꯣꯕꯒꯤ ꯀꯥꯔꯗ 48, ꯃꯗꯨꯒꯥ ꯂꯣꯌꯅꯅ ꯑꯦꯁ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯖꯣꯀꯔ ꯑꯃꯥ꯫ ꯀꯥꯔꯗ ꯑꯃꯈꯛꯅ 47 ꯗꯒꯤ 1 ꯄꯤ, ꯀꯥꯔꯗ ꯑꯅꯤꯅ 23 ꯗꯒꯤ 1, ꯑꯍꯨꯃꯅ 15 ꯗꯒꯤ 1, ꯃꯔꯤꯅ 11 ꯗꯒꯤ 1, ꯇꯔꯨꯛꯅ 7 ꯗꯒꯤ 1, ꯅꯤꯄꯥꯟꯅ 5 ꯗꯒꯤ 1, ꯇꯔꯥꯅꯤꯊꯣꯏꯅ 3 ꯗꯒꯤ 1, ꯇꯔꯥꯅꯤꯇꯔꯨꯛꯅ 2 ꯗꯒꯤ 1 ꯑꯃꯁꯨꯡ ꯀꯨꯟꯃꯔꯤꯅ 1 ꯗꯒꯤ 1꯫ ꯀꯔꯤ ꯅꯤꯌꯝꯅ ꯄꯦꯑꯥꯎꯠꯁꯤꯡꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯁꯦꯝꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯃꯜ ꯀꯌꯥ ꯂꯩꯕꯒꯦ?

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ ꯀꯥꯔꯗ n ꯗ ꯊꯝꯕ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ (48 − n)/n ꯗꯒꯤ 1 ꯄꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯃꯜ 2/50 = 4% ꯂꯩ꯫

   ꯕꯦꯠ ꯈꯔꯗ ꯅꯤꯌꯝ ꯑꯗꯨ ꯌꯦꯡꯕꯤꯌꯨ: 47/1 = 47, 36/12 = 3, 32/16 = 2, 24/24 = 1꯫ ꯃꯗꯨ ꯃꯥꯄꯟ ꯄꯨꯝꯅꯃꯛꯇ ꯆꯥꯟꯅꯩ꯫ ꯅꯤꯌꯝ ꯑꯗꯨꯅ ꯆꯛꯔ ꯑꯗꯨꯗ ꯄꯣꯀꯦꯠ 48 ꯂꯩꯕꯒꯨꯝ ꯃꯃꯜ ꯂꯧꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯦꯁ ꯑꯃꯁꯨꯡ ꯖꯣꯀꯔ ꯑꯗꯨ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠ ꯑꯅꯤꯅꯤ, ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔꯗ 0 ꯑꯃꯁꯨꯡ 00 ꯑꯣꯏꯕꯒꯨꯝꯅ꯫

   50 ꯒꯤ ꯃꯅꯨꯡꯗ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠ ꯑꯅꯤꯅ 4% ꯒꯤ ꯑꯦꯖ ꯄꯤ꯫ “ꯌꯨꯔꯣꯄꯤꯌꯟ” ꯃꯈꯜ ꯑꯃꯅ ꯖꯣꯀꯔ ꯑꯗꯨ ꯂꯧꯊꯣꯛꯇꯨꯅ ꯄꯦꯑꯥꯎꯠꯁꯤꯡ ꯍꯣꯡꯗꯣꯀꯗꯦ: 49 ꯗ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠ ꯑꯃꯥ, 2.04% ꯒꯤ ꯑꯦꯖ꯫

2. ꯁꯨꯄꯔ 62 ꯗ ꯈꯅꯕ ꯗꯤꯖꯤꯠ ꯑꯃꯥ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯁꯤꯡꯗ ꯊꯣꯛꯀꯅꯤ ꯍꯥꯌꯅ ꯕꯦꯠ ꯊꯝꯕ ꯌꯥꯏ꯫ ꯃꯇꯧ ꯑꯁꯨꯝꯕ ꯕꯦꯠ ꯑꯗꯨ ꯃꯍꯧꯁꯥꯒꯤ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔ ꯑꯃꯒꯤꯗꯃꯛ ꯁꯦꯝꯕꯤꯌꯨ꯫ 1 ꯗꯒꯤ 36 ꯐꯥꯑꯣꯕꯒꯤ ꯃꯁꯤꯡꯁꯤꯡꯒꯤ ꯃꯅꯨꯡꯗ ꯀꯌꯥꯗ ꯗꯤꯖꯤꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯌꯥꯎꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯄꯦꯑꯥꯎꯠꯅ ꯃꯍꯧꯁꯥꯒꯤ 5.26% ꯊꯝꯒꯅꯤ?

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ ꯃꯁꯤꯡ 3 ꯅꯠꯔꯒ 4 ꯂꯩꯕ ꯗꯤꯖꯤꯠꯁꯤꯡꯈꯛꯇꯅ ꯃꯄꯨꯡ ꯐꯥꯕ ꯄꯦꯑꯥꯎꯠ ꯐꯪꯏ (11 ꯗꯒꯤ 1 ꯑꯃꯁꯨꯡ 8 ꯗꯒꯤ 1)꯫ ꯗꯤꯖꯤꯠ 1, 2 ꯑꯃꯁꯨꯡ 3 ꯕꯨ ꯃꯄꯨꯡ ꯐꯥꯕ ꯆꯤꯞꯁꯤꯡꯗꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯨꯝꯃꯤꯟꯅ ꯄꯤꯕ ꯉꯃꯗꯦ꯫

   ꯃꯁꯤꯡꯁꯤꯡ ꯃꯁꯤꯡ ꯊꯤꯕꯤꯌꯨ꯫ ꯗꯤꯖꯤꯠ 1 ꯑꯁꯤ 1, 10 ꯗꯒꯤ 19, 21 ꯑꯃꯁꯨꯡ 31 ꯗ ꯂꯩ: ꯃꯁꯤꯡ 13꯫ ꯗꯤꯖꯤꯠ 2 ꯁꯨ ꯃꯁꯤꯡ 13 ꯗ ꯂꯩ ꯑꯃꯁꯨꯡ ꯗꯤꯖꯤꯠ 3 ꯃꯁꯤꯡ 10 ꯗ꯫ ꯗꯤꯖꯤꯠ 4, 5 ꯑꯃꯁꯨꯡ 6 ꯈꯨꯗꯤꯡꯃꯛ ꯃꯁꯤꯡ ꯃꯔꯤꯗ ꯂꯩ (4, 14, 24, 34), ꯑꯃꯁꯨꯡ 7, 8 ꯑꯃꯁꯨꯡ 9 ꯈꯨꯗꯤꯡꯃꯛ ꯑꯍꯨꯃꯗ꯫

   ꯃꯁꯤꯡ n ꯗ ꯊꯝꯕ ꯕꯦꯠ ꯑꯃꯅ (36 − n)/n ꯗꯒꯤ 1 ꯄꯤꯔꯕꯗ ꯑꯃꯦꯔꯤꯀꯟ ꯑꯦꯖ ꯑꯗꯨ ꯊꯝꯃꯤ꯫ ꯃꯗꯨꯅ ꯃꯁꯤꯡ ꯃꯔꯤꯒꯤꯗꯃꯛ 8 ꯗꯒꯤ 1 ꯑꯃꯁꯨꯡ ꯑꯍꯨꯃꯒꯤꯗꯃꯛ 11 ꯗꯒꯤ 1 ꯄꯤ, ꯑꯅꯤꯃꯛ ꯃꯄꯨꯡ ꯐꯥꯕꯅꯤ꯫ ꯃꯁꯤꯡ 13 ꯒꯤꯗꯃꯛ 23/13, ꯈꯟꯊꯕꯗ 1.77 ꯗꯒꯤ 1, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯡ 10 ꯒꯤꯗꯃꯛ 2.6 ꯗꯒꯤ 1 ꯄꯤ꯫ 1.77 ꯕꯨ 7 ꯗꯒꯤ 4 ꯐꯥꯑꯣꯕ ꯍꯟꯊꯍꯜꯂꯕꯗ ꯕꯦꯠ ꯑꯗꯨꯒꯤ ꯃꯃꯜ 5.92% ꯂꯩ; 2 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯍꯥꯞꯂꯕꯗ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯗꯨꯅ 2.63% ꯒꯤ ꯑꯦꯖ ꯐꯪꯏ꯫ 2.6 ꯕꯨ 5 ꯗꯒꯤ 2 ꯐꯥꯑꯣꯕ ꯍꯟꯊꯍꯜꯂꯕꯗ 7.89% ꯑꯣꯏ꯫

   ꯗꯤꯖꯤꯠ 0 ꯗꯤ ꯈꯅꯕꯒꯤ ꯋꯥꯐꯃꯅꯤ: 10, 20 ꯑꯃꯁꯨꯡ 30 ꯈꯛꯇꯅ 11 ꯗꯒꯤ 1 ꯄꯤ, 5.26% ꯗ; 0 ꯑꯃꯁꯨꯡ 00 ꯍꯥꯄꯆꯤꯜꯂꯕꯗ ꯃꯁꯤꯡ ꯃꯉꯥꯒꯤ ꯕꯦꯠ ꯑꯣꯏꯔꯛꯏ, 6 ꯗꯒꯤ 1, 7.89% ꯗ, ꯕꯥꯁ꯭ꯀꯦꯠꯕꯦꯠꯕꯥꯁ꯭ꯀꯦꯠꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔꯗ: ꯆꯤꯞ ꯑꯃꯅ 0, 1, 2, 3, 8:1 ꯄꯦꯑꯥꯎꯠ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯑꯍꯥꯅꯕ ꯃꯔꯤ, ꯀꯥꯠꯔ ꯄ꯭ꯔꯦꯃꯤꯌꯦ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯒꯨꯝꯅ꯫

   ꯗꯤꯖꯤꯠꯃꯁꯤꯡꯁꯤꯡꯅꯤꯌꯝꯅ ꯍꯥꯌꯔꯤꯕꯄꯤꯕ ꯌꯥꯕꯍꯥꯎꯁ ꯑꯦꯖ

   1, 2131.77 ꯗꯒꯤ 17 ꯗꯒꯤ 45.92%

   3102.6 ꯗꯒꯤ 15 ꯗꯒꯤ 27.89%

   4, 5, 648 ꯗꯒꯤ 18 ꯗꯒꯤ 15.26%

   7, 8, 9311 ꯗꯒꯤ 111 ꯗꯒꯤ 15.26%

3. 100 ꯇꯨ 1 ꯔꯨꯂꯦꯠꯅ ꯃꯁꯤꯡ 100 ꯑꯃꯁꯨꯡ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯁꯤꯝꯕꯣꯜ 5 ꯂꯩꯕ ꯆꯛꯔ ꯑꯃꯗ ꯕꯦꯠ ꯀꯌꯥꯗ (100 − n)/n ꯗꯒꯤ 1 ꯄꯤ꯫ ꯃꯁꯤꯒꯤ ꯕꯦꯠꯁꯤꯡꯅ ꯄꯣꯀꯦꯠ 1, 2, 3, 4, 5, 10, 15, 20 ꯅꯠꯔꯒ 50 ꯀꯨꯞꯏ ꯑꯃꯁꯨꯡ 100, 49, 32, 24, 19, 9, 11 ꯗꯒꯤ 2, 4 ꯑꯃꯁꯨꯡ 1 ꯗꯒꯤ 1 ꯄꯤ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯄꯣꯀꯦꯠ 15 ꯒꯤ ꯑꯦꯚꯦꯅ꯭ꯌꯨꯅ ꯅꯤꯌꯝ ꯑꯗꯨ ꯊꯨꯒꯥꯏ꯫ ꯑꯇꯣꯞꯄ ꯀꯔꯤ ꯕꯦꯠꯅ ꯊꯨꯒꯥꯏꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯒꯤ ꯃꯃꯜ ꯀꯌꯥ ꯂꯩꯕꯒꯦ?

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ ꯄꯣꯀꯦꯠ ꯑꯍꯨꯃꯒꯤ ꯕꯦꯠ: ꯅꯤꯌꯝꯅ 32⅓ ꯗꯒꯤ 1 ꯍꯥꯌꯔꯤ, ꯃꯁꯤꯅ 32 ꯗꯒꯤ 1 ꯄꯤ, ꯑꯃꯁꯨꯡ 4.76% ꯒꯤ ꯃꯍꯨꯠꯇ 5.71% ꯃꯃꯜ ꯂꯩ꯫

   ꯄꯦꯑꯥꯎꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯅꯤꯌꯝ ꯑꯗꯨꯒꯥ ꯆꯥꯡꯗꯝꯅꯕꯤꯌꯨ: 98/2 = 49, 96/4 = 24, 95/5 = 19, 90/10 = 9, 80/20 = 4 ꯑꯃꯁꯨꯡ 50/50 = 1 ꯄꯨꯝꯅꯃꯛ ꯆꯥꯟꯅꯩ꯫ ꯄꯣꯀꯦꯠ ꯑꯍꯨꯃꯒꯤꯗꯃꯛ ꯅꯤꯌꯝꯅ 97/3 = 32⅓ ꯄꯤ, ꯃꯁꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯆꯤꯞ ꯑꯃꯠꯇꯅ ꯄꯤꯕ ꯉꯃꯗꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ 32 ꯐꯥꯑꯣꯕ ꯍꯟꯊꯍꯜꯂꯤ꯫

   ꯕꯦꯠ ꯑꯗꯨꯅ ꯁ꯭ꯄꯤꯟ 105 ꯗ ꯑꯃꯨꯛ 3 ꯃꯥꯏꯄꯥꯛꯏ ꯑꯃꯁꯨꯡ ꯊꯝꯂꯕ ꯁꯦꯜ ꯌꯥꯎꯅ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 33 ꯍꯜꯂꯛꯏ: ꯊꯝꯂꯕ 105 ꯈꯨꯗꯤꯡꯗ 3 × 33 = ꯌꯨꯅꯤꯠ 99 ꯍꯜꯂꯛꯏ, 6/105 = 5.71% ꯃꯥꯡꯏ꯫

4. ꯐꯣꯡꯗꯣꯀꯈꯤꯕ ꯗꯤꯖꯥꯏꯟ ꯑꯃꯥ ꯑꯣꯏꯔꯤꯕ ꯔꯨꯂꯦꯠ 73 ꯗ ꯃꯁꯤꯡ 72 ꯑꯃꯁꯨꯡ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯂꯩ, ꯑꯃꯁꯨꯡ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ (72 − n)/n ꯗꯒꯤ 1 ꯄꯤ꯫ ꯃꯁꯤꯒꯤ ꯒ꯭ꯔꯦ ꯃꯆꯨꯒꯤ ꯃꯁꯤꯡ 24 ꯑꯗꯨ ꯆꯤꯞ 14 ꯅ ꯀꯨꯞꯄ ꯌꯥꯏ: ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ 4 ꯑꯃꯁꯨꯡ ꯁ꯭ꯞꯂꯤꯠꯕꯦꯠꯁ꯭ꯞꯂꯤꯠꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯅꯤ, 17:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 10꯫ ꯆꯤꯞ 14 ꯒꯤ ꯕꯦꯠ ꯑꯗꯨꯒꯤ ꯃꯃꯜ ꯀꯌꯥ ꯂꯩꯕꯒꯦ?

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ ꯆꯤꯞ 14 ꯒꯤ 1.37%, ꯆꯛꯔ ꯑꯗꯨꯒꯤ ꯑꯇꯩ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯒꯨꯝꯅ꯫

   ꯁꯥꯡꯕ ꯂꯝꯕꯤ: ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯅ 71 ꯗꯒꯤ 1 ꯑꯃꯁꯨꯡ ꯁ꯭ꯞꯂꯤꯠꯅ 35 ꯗꯒꯤ 1 ꯄꯤ꯫ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯃꯁꯤꯡ 4 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ ꯑꯃꯥ ꯊꯣꯛꯂꯕꯗ, ꯅꯍꯥꯛꯅ 71 ꯃꯥꯏꯄꯥꯛꯏ ꯑꯃꯁꯨꯡ ꯑꯇꯣꯞꯄ ꯆꯤꯞ 13 ꯃꯥꯡꯏ: +58꯫ ꯁ꯭ꯞꯂꯤꯠ ꯃꯁꯤꯡ 20 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ ꯑꯃꯥ ꯊꯣꯛꯂꯕꯗ: +35 − 13 = +22꯫ ꯑꯇꯣꯞꯄ ꯄꯣꯀꯦꯠ 49 ꯗ ꯅꯍꯥꯛꯅ 14 ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯏ꯫ ꯁ꯭ꯄꯤꯟ 73 ꯗ ꯑꯦꯚꯔꯦꯖꯗ: 4 × 58 + 20 × 22 − 49 × 14 = 232 + 440 − 686 = −14 ꯌꯨꯅꯤꯠ, ꯃꯁꯤ ꯆꯤꯞ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ 1/73 ꯅꯤ꯫

   ꯌꯧꯕ ꯂꯝꯕꯤ: ꯐꯪꯒꯗꯕ ꯃꯃꯜꯁꯤꯡꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯄꯨꯟꯁꯤꯟꯕ ꯌꯥꯏ꯫ ꯆꯤꯞ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯁꯥꯒꯤ 1/73 ꯃꯥꯡꯕ ꯃꯍꯧꯁꯥꯒꯤ ꯕꯦꯠ ꯑꯃꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯆꯤꯞ 14 ꯅ 14/73 ꯃꯥꯡꯏ꯫ ꯕꯦꯠꯁꯤꯡ ꯄꯨꯟꯁꯤꯟꯕꯅ ꯃꯍꯩꯁꯤꯡ ꯀꯔꯝꯅ ꯁꯟꯗꯣꯛꯂꯤꯕꯒꯦ ꯍꯥꯌꯕꯗꯨ ꯍꯣꯡꯗꯣꯀꯏ, ꯃꯃꯜ ꯑꯗꯨ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯍꯣꯡꯗꯣꯀꯄ ꯉꯃꯗꯦ꯫

5. ꯁꯨꯄꯔ 62 ꯗ ꯃꯁꯤꯡ 60, 0 ꯑꯃꯁꯨꯡ 00 ꯂꯩ, ꯑꯃꯁꯨꯡ (60 − n)/n ꯗꯒꯤ 1 ꯄꯤ꯫ ꯃꯁꯤꯒꯤ ꯗꯤꯖꯥꯏꯅꯔꯁꯤꯡꯅ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠ ꯑꯃꯥ, ꯑꯍꯨꯝ ꯑꯃꯁꯨꯡ ꯃꯔꯤ ꯂꯩꯕ ꯃꯈꯂꯁꯤꯡꯁꯨ ꯌꯦꯛꯈꯤ꯫ ꯑꯦꯂꯐꯥꯕꯦꯇꯤꯛ ꯔꯨꯂꯦꯠꯅ ꯄꯣꯀꯦꯠ 25 ꯗ (24 − n)/n ꯗꯒꯤ 1 ꯄꯤ, ꯑꯃꯁꯨꯡ Y ꯑꯃꯁꯨꯡ Z ꯃꯁꯥꯒꯤ ꯄꯣꯀꯦꯠ ꯇꯣꯉꯥꯟꯅ ꯂꯩꯕ ꯃꯈꯜ ꯑꯃꯁꯨ ꯂꯩ꯫ ꯃꯉꯥ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯃꯃꯜ ꯊꯤꯕꯤꯌꯨ꯫

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ ꯖꯤꯔꯣ ꯑꯃꯗꯒꯤ ꯃꯔꯤ ꯐꯥꯑꯣꯕ: 1.64%, 3.23%, 4.76% ꯑꯃꯁꯨꯡ 6.25%꯫ Y ꯑꯃꯁꯨꯡ Z ꯇꯣꯉꯥꯟꯅ ꯂꯩꯕ ꯑꯦꯂꯐꯥꯕꯦꯇꯤꯛ: 7.69%꯫

   ꯃꯈꯣꯌ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯄꯦꯑꯥꯎꯠꯁꯤꯡ ꯊꯝꯃꯤ ꯑꯃꯁꯨꯡ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠꯀꯤ ꯃꯁꯤꯡ ꯈꯛꯇ ꯍꯣꯡꯗꯣꯀꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯦꯖ ꯑꯗꯨ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠ ÷ ꯄꯣꯀꯦꯠ ꯄꯨꯝꯅꯃꯛ ꯑꯣꯏ꯫

   ꯖꯤꯔꯣ ꯑꯃꯥ, ꯄꯣꯀꯦꯠ 61: 1/61 = 1.64%꯫ ꯑꯅꯤ, ꯄꯣꯀꯦꯠ 62: 2/62 = 3.23%꯫ ꯑꯍꯨꯝ, ꯄꯣꯀꯦꯠ 63: 3/63 = 4.76%꯫ ꯃꯔꯤ, ꯄꯣꯀꯦꯠ 64: 4/64 = 6.25%꯫ ꯍꯥꯄꯆꯤꯜꯂꯕ ꯖꯤꯔꯣ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯈꯟꯊꯕꯗ ꯄꯣꯏꯟꯠ ꯑꯃꯥ ꯁꯔꯨꯛ ꯍꯥꯟꯗ ꯃꯃꯜ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ꯫

   ꯑꯦꯂꯐꯥꯕꯦꯇꯤꯛꯅ ꯃꯌꯦꯛ 24 ꯂꯩꯕꯒꯨꯝ ꯄꯦꯑꯥꯎꯠ ꯄꯤ꯫ Y ꯑꯃꯁꯨꯡ Z ꯄꯣꯀꯦꯠ ꯑꯃꯗ ꯂꯩꯃꯤꯟꯅꯔꯕꯗ ꯀꯦꯁꯤꯅꯣꯒꯤ 25 ꯗ 1 ꯂꯩ, 4%꯫ Y ꯑꯃꯁꯨꯡ Z ꯇꯣꯉꯥꯟꯅ ꯂꯩꯔꯕꯗ 26 ꯗ 2 ꯂꯩ, 7.69%, ꯇ꯭ꯔꯤꯄꯜ ꯖꯤꯔꯣ ꯆꯛꯔ ꯑꯃꯒꯨꯝꯅ꯫ ꯄꯣꯀꯦꯠ ꯑꯃꯥ ꯑꯅꯤꯗ ꯈꯥꯌꯕꯅ ꯃꯃꯜ ꯑꯗꯨ ꯈꯟꯊꯕꯗ ꯑꯅꯤ ꯁꯔꯨꯛ ꯑꯣꯏꯍꯜꯂꯦ꯫

   ꯆꯛꯔꯄꯣꯀꯦꯠꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠꯍꯥꯎꯁ ꯑꯦꯖ

   ꯃꯁꯤꯡ 60, ꯖꯤꯔꯣ ꯑꯃꯥ6111.64%

   ꯁꯨꯄꯔ 626223.23%

   ꯃꯁꯤꯡ 60, ꯖꯤꯔꯣ ꯑꯍꯨꯝ6334.76%

   ꯁꯨꯄꯔ 646446.25%

   ꯑꯦꯂꯐꯥꯕꯦꯇꯤꯛ2514.00%

   ꯑꯦꯂꯐꯥꯕꯦꯇꯤꯛ, Y ꯑꯃꯁꯨꯡ Z ꯇꯣꯉꯥꯟꯅ2627.69%

6. ꯑꯔꯤꯕ ꯆꯛꯔ ꯑꯃꯗ ꯄꯣꯀꯦꯠ 18 ꯂꯩ: 1 ꯗꯒꯤ 16, 0 ꯑꯃꯁꯨꯡ 00꯫ ꯕꯤꯖꯣꯔ ꯃꯁꯤꯡꯁꯤꯡ ꯑꯃꯁꯨꯡ 0 ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯖꯣꯔ ꯃꯁꯤꯡꯁꯤꯡ ꯑꯃꯁꯨꯡ 00 ꯑꯃꯨꯕꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯑꯃꯁꯨꯡ ꯃꯁꯤꯡ 16 ꯑꯗꯨ ꯔꯣ 4 ꯑꯃꯁꯨꯡ ꯀꯂꯝ 4 ꯂꯩꯕ ꯂꯦꯑꯥꯎꯠꯈꯨꯠꯂꯥꯏꯂꯦꯑꯥꯎꯠꯇꯦꯕꯜꯗ ꯏꯔꯕ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯒ꯭ꯔꯤꯗ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯇꯦꯕꯜ, ꯐꯦꯜꯠ, ꯀ꯭ꯂꯣꯊ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯂꯩ꯫ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯑꯦꯖ ꯑꯃꯠꯇꯥ ꯄꯤꯕ ꯄꯦꯑꯥꯎꯠ ꯇꯦꯕꯜꯁꯦꯜꯄꯦꯑꯥꯎꯠ ꯇꯦꯕꯜꯕꯦꯠ ꯅꯠꯔꯒ ꯃꯍꯩ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯀꯌꯥ ꯄꯤꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯂꯤꯁ꯭ꯠ꯫ ꯃꯦꯁꯤꯅꯁꯤꯡ ꯑꯃꯁꯨꯡ ꯁꯥꯏꯗ ꯕꯦꯠꯁꯤꯡꯗ ꯍꯥꯎꯁ ꯑꯦꯖ ꯂꯦꯞꯄꯤꯕ ꯃꯐꯝꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯁꯦꯝꯕꯤꯌꯨ꯫ ꯑꯃꯁꯨꯡ 0 ꯑꯁꯤ ꯑꯉꯥꯡꯕ ꯑꯣꯏꯔꯕꯁꯨ ꯀꯔꯤꯒꯤ ꯑꯉꯥꯡꯕꯗ ꯊꯝꯕ ꯕꯦꯠ ꯃꯥꯏꯊꯤꯍꯅꯒꯗꯕꯅꯣ?

   ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

   ꯄꯥꯎꯈꯨꯝ (16 − n)/n ꯗꯒꯤ 1 ꯄꯤꯕꯤꯌꯨ: ꯃꯁꯤꯡ ꯑꯃꯗ 15 ꯗꯒꯤ 1, ꯑꯅꯤꯗ 7, ꯃꯔꯤꯗ 3, ꯅꯤꯄꯥꯟꯗ 1꯫ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯃꯜ 11.11% ꯂꯩ꯫ 0 ꯅ ꯑꯉꯥꯡꯕꯒꯤ ꯕꯦꯠ ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ, ꯑꯉꯥꯡꯕ ꯑꯁꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯕꯦꯠ ꯑꯃꯥ ꯑꯣꯏꯔꯛꯀꯅꯤ꯫

   0 ꯑꯃꯁꯨꯡ 00 ꯂꯩꯇꯕꯒꯨꯝ ꯆꯛꯔ ꯑꯗꯨꯒꯤ ꯃꯃꯜ ꯂꯧꯕꯤꯌꯨ꯫ ꯃꯁꯤꯡ n ꯗ ꯊꯝꯕ ꯕꯦꯠ ꯑꯃꯅ 18 ꯗ ꯑꯃꯨꯛ n ꯃꯥꯏꯄꯥꯛꯏ ꯑꯃꯁꯨꯡ (16 − n)/n ꯗꯒꯤ 1 ꯄꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯊꯝꯂꯕ 18 ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜ ꯌꯥꯎꯅ ꯌꯨꯅꯤꯠ 16 ꯍꯜꯂꯛꯏ꯫ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯃꯜ 2/18, 11.11% ꯂꯩ꯫

   ꯂꯦꯑꯥꯎꯠꯀꯤ ꯃꯍꯧꯁꯥꯒꯤ ꯕꯦꯠꯁꯤꯡꯅ ꯃꯄꯨꯡ ꯐꯥꯕ ꯃꯁꯤꯡ ꯄꯤ: ꯃꯁꯤꯡ ꯑꯃꯥ 15 ꯗꯒꯤ 1, ꯃꯅꯥꯛ ꯃꯅꯥꯛꯇ ꯂꯩꯕ ꯑꯅꯤ 7 ꯗꯒꯤ 1, ꯃꯔꯤꯒꯤ ꯔꯣ ꯑꯃꯥ ꯅꯠꯔꯒ ꯀꯂꯝꯕꯦꯠꯀꯂꯝꯂꯦꯑꯥꯎꯠꯀꯤ ꯊꯣꯡꯅꯥꯡꯒꯤ ꯀꯂꯝ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ 3 ꯗꯒꯤ 1, ꯑꯃꯁꯨꯡ ꯔꯣ ꯑꯅꯤ, ꯅꯠꯔꯒ ꯕꯤꯖꯣꯔ, ꯖꯣꯔ, ꯑꯅꯦꯝꯕ ꯅꯠꯔꯒ ꯑꯋꯥꯡꯕ ꯅꯤꯄꯥꯟ, 1 ꯗꯒꯤ 1꯫ ꯃꯁꯤꯡ ꯑꯍꯨꯃꯒꯤ ꯕꯦꯠ ꯑꯃꯅ 4⅓ ꯗꯒꯤ 1 ꯃꯊꯧ ꯇꯥꯏ; 4 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯍꯟꯊꯍꯜꯂꯕꯗ ꯃꯃꯜ 16.67% ꯂꯩ꯫

   ꯑꯉꯥꯡꯕꯅ ꯕꯤꯖꯣꯔ ꯃꯁꯤꯡ ꯅꯤꯄꯥꯟ ꯀꯨꯞꯏ꯫ 0, ꯑꯉꯥꯡꯕ ꯑꯣꯏꯕꯅ, ꯑꯉꯥꯡꯕꯒꯤ ꯕꯦꯠꯁꯨ ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ, ꯑꯉꯥꯡꯕꯅ ꯄꯣꯀꯦꯠ 18 ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ 9 ꯀꯨꯞꯀꯅꯤ 1 ꯗꯒꯤ 1 ꯗ: ꯑꯦꯖ ꯑꯃꯠꯇꯥ ꯂꯩꯇꯕ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯀꯅꯥꯒꯨꯝꯕ ꯃꯥꯏꯀꯩ ꯑꯃꯠꯇꯗ ꯑꯦꯖ ꯂꯩꯇꯕ ꯁꯥꯟꯅꯕ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯖꯤꯔꯣꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ꯫ ꯀꯦꯁꯤꯅꯣꯒꯤ ꯄꯣꯀꯦꯠꯁꯤꯡꯅ ꯃꯈꯣꯌ ꯃꯁꯥꯗ ꯊꯝꯕ ꯕꯦꯠ ꯅꯠꯇꯕ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯥꯏꯊꯤꯍꯟꯗꯨꯅ ꯈꯛꯇꯅ ꯃꯈꯣꯌꯒꯤ ꯑꯦꯖ ꯐꯪꯏ꯫