Математика и информатика. Решение логико-познавательных задач. Учебное пособие для студентов вузов

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ǶǺ ǨǪǺǶǸǨ

ɋɨɜɪɟɦɟɧɧɨɟ ɪɨɫɫɢɣɫɤɨɟ ɨɛɳɟɫɬɜɨ ɫɬɚɜɢɬ ɩɟɪɟɞ ɜɵɫɲɟɣ ɲɤɨɥɨɣ ɡɚɞɚɱɭ ɩɨɞɝɨɬɨɜɤɢ ɜɵɫɨɤɨɢɧɬɟɥɥɟɤɬɭɚɥɶɧɵɯ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɧɟ ɬɨɥɶɤɨ ɜɨɨɪɭɠɢɜ ɢɯ ɧɨɜɟɣɲɢɦɢ ɞɨɫɬɢɠɟɧɢɹɦɢ ɧɚɭɤɢ ɢ ɬɟɯɧɢɤɢ ɢ ɫɨɜɟɪɲɟɧɧɵɦɢ ɦɟɬɨɞɚɦɢ ɧɚɭɱɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɧɨ ɢ ɫɮɨɪɦɢɪɨɜɚɜ ɭ ɧɢɯ ɜɵɫɨɤɭɸ ɤɭɥɶɬɭɪɭ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɤɭɥɶɬɭɪɵ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ ɫɬɚɧɨɜɢɬɫɹ ɜɚɠɧɟɣɲɢɦ ɚɫɩɟɤɬɨɦ ɜ ɩɨɞɝɨɬɨɜɤɟ ɛɭɞɭɳɢɯ ɫɩɟɰɢɚɥɢɫɬɨɜ, ɬɚɤ ɤɚɤ ɩɨɦɨɝɚɟɬ ɜɵɩɭɫɤɧɢɤɚɦ ɜɭɡɨɜ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɬɶ ɮɨɪɦɚɥɶɧɵɣ ɚɩɩɚɪɚɬ ɦɵɲɥɟɧɢɹ, ɫɢɫɬɟɦɚɬɢɡɢɪɨɜɚɬɶ ɢ ɤɥɚɫɫɢɮɢɰɢɪɨɜɚɬɶ ɷɦɩɢɪɢɱɟɫɤɢɟ ɡɧɚɧɢɹ, ɚ ɬɚɤɠɟ ɩɪɚɜɢɥɶɧɨ ɨɰɟɧɢɜɚɬɶ ɢɫɬɢɧɧɭɸ ɫɭɳɧɨɫɬɶ ɹɜɥɟɧɢɣ ɢ ɩɪɨɰɟɫɫɨɜ, ɜ ɫɨɜɪɟɦɟɧɧɨɦ ɨɛɳɟɫɬɜɟ.

ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɨɫɨɛɧɨɫɬɶ ɥɨɝɢɱɟɫɤɢ ɦɵɫɥɢɬɶ ɮɨɪɦɢɪɭɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɠɢɡɧɟɞɟɹɬɟɥɶɧɨɫɬɢ ɱɟɥɨɜɟɤɚ ɢ ɞɥɹ ɟɟ ɩɨɥɧɨɰɟɧɧɨɝɨ ɪɚɡɜɢɬɢɹ ɧɟɨɛɯɨɞɢɦɵ ɫɩɟɰɢɚɥɶɧɵɟ ɭɫɥɨɜɢɹ.

ɂɡɭɱɟɧɢɟ ɮɨɪɦɢɪɨɜɚɧɢɹ ɤɭɥɶɬɭɪɵ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ ɩɪɨɜɨɞɢɬɫɹ ɭɱɟɧɵɦɢ — ɩɟɞɚɝɨɝɚɦɢ, ɩɫɢɯɨɥɨɝɚɦɢ, ɦɚɬɟɦɚɬɢɤɚɦɢ — ɧɚ ɩɪɨɬɹɠɟɧɢɢ ɦɧɨɝɢɯ ɥɟɬ. Ⱥɧɚɥɢɡ ɷɬɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɨɤɚɡɚɥ, ɱɬɨ ɩɪɢ ɬɪɚɞɢɰɢɨɧɧɨɦ ɨɛɭɱɟɧɢɢ ɢ ɫɪɟɞɧɹɹ, ɢ ɜɵɫɲɚɹ ɲɤɨɥɚ ɧɟɞɨɫɬɚɬɨɱɧɨ ɜɨɨɪɭɠɚɟɬ ɨɛɭɱɚɸɳɢɯɫɹ ɩɪɢɟɦɚɦɢ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ.

ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɡɧɚɧɢɹ ɢ ɭɦɟɧɢɹ ɤɚɤ ɟɞɢɧɢɰɵ ɪɟɡɭɥɶɬɚɬɚ ɨɛɪɚɡɨɜɚɬɟɥɶɧɨɝɨ ɩɪɨɰɟɫɫɚ ɧɟɨɛɯɨɞɢɦɵ, ɧɨ ɧɟ ɞɨɫɬɚɬɨɱɧɵ ɞɥɹ ɭɫɩɟɲɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱ, ɤɨɬɨɪɵɟ ɫɬɚɜɢɬ ɩɟɪɟɞ ɱɟɥɨɜɟɤɨɦ ɫɨɜɪɟɦɟɧɧɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɨɛɳɟɫɬɜɨ. Ɉɫɨɛɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢɨɛɪɟɬɚɟɬ ɫɩɨɫɨɛɧɨɫɬɶ ɱɟɥɨɜɟɤɚ ɩɪɢɦɟɧɹɬɶ ɨɛɨɛɳɟɧɧɵɟ ɡɧɚɧɢɹ ɢ ɭɦɟɧɢɹ ɞɥɹ ɪɚɡɪɟɲɟɧɢɹ ɩɪɨɛɥɟɦɧɵɯ ɫɢɬɭɚɰɢɣ, ɤɨɬɨɪɵɟ ɪɟɝɭɥɹɪɧɨ ɜɨɡɧɢɤɚɸɬ ɜ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɥɸɛɨɝɨ ɫɩɟɰɢɚɥɢɫɬɚ.

Ʌɭɱɲɢɦ ɩɪɢɦɟɪɨɦ ɩɪɨɛɥɟɦɧɨɣ ɫɢɬɭɚɰɢɢ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɥɨɝɢɤɨɩɨɡɧɚɜɚɬɟɥɶɧɚɹ ɡɚɞɚɱɚ, ɩɪɢ ɪɟɲɟɧɢɢ ɤɨɬɨɪɨɣ ɨɛɭɱɚɸɳɢɣɫɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɵɬɚɟɬɫɹ ɩɪɟɨɞɨɥɟɬɶ ɫɢɬɭɚɰɢɸ «ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɝɨ ɡɚɬɪɭɞɧɟɧɢɹ», ɬɨ ɟɫɬɶ ɪɚɡɪɟɲɢɬɶ ɩɪɨɛɥɟɦɧɭɸ ɫɢɬɭɚɰɢɸ, ɚ ɧɟ ɩɨɥɭɱɢɬɶ ɝɨɬɨɜɨɟ ɪɟɲɟɧɢɟ.

Ʌɨɝɢɤɨ-ɩɨɡɧɚɜɚɬɟɥɶɧɵɟ ɡɚɞɚɱɢ, ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɜ ɩɨɫɨɛɢɢ, ɨɯɜɚɬɵɜɚɸɬ ɜɚɠɧɟɣɲɢɟ ɬɟɦɵ ɭɱɟɛɧɨɣ ɞɢɫɰɢɩɥɢɧɵ «Ɇɚɬɟɦɚɬɢɤɚ ɢ ɢɧɮɨɪɦɚɬɢɤɚ». Ⱦɚɧɧɚɹ ɞɢɫɰɢɩɥɢɧɚ ɜ ɛɨɥɶɲɟɣ ɫɬɟɩɟɧɢ, ɱɟɦ ɞɪɭɝɢɟ ɭɱɟɛɧɵɟ ɞɢɫɰɢɩɥɢɧɵ, ɜɥɢɹɟɬ ɧɚ ɮɨɪɦɢɪɨɜɚɧɢɟ ɢ ɪɚɡɜɢɬɢɟ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ, ɬɚɤ ɤɚɤ ɭɱɟɛɧɵɣ ɦɚɬɟɪɢɚɥ ɷɬɨɣ ɞɢɫɰɢɩɥɢɧɵ ɢɦɟɟɬ ɜɵɫɨɤɢɣ ɭɪɨɜɟɧɶ ɫɢɫɬɟɦɚɬɢɡɚɰɢɢ ɢ ɚɥɝɨɪɢɬɦɢɡɚɰɢɢ, ɚ ɬɚɤɠɟ ɢɡɨɛɢɥɭɟɬ ɥɨɝɢɱɟɫɤɢɦɢ ɤɨɧɫɬɪɭɤɰɢɹɦɢ ɢ ɮɨɪɦɚɥɢɡɨɜɚɧɧɵɦɢ ɦɨɞɟɥɹɦɢ.

Ɂɚɞɚɱɢ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɟ ɜ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ, ɜɚɪɶɢɪɭɸɬɫɹ ɩɨ ɫɬɟɩɟɧɢ ɫɥɨɠɧɨɫɬɢ. Ɍɚɤ, ɡɚɞɚɱɢ ɩɟɪɜɨɝɨ ɭɪɨɜɧɹ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɵ ɢ ɬɪɟ-

3

ɛɭɸɬ ɛɚɡɨɜɨɝɨ ɨɛɴɟɦɚ ɡɧɚɧɢɣ. Ⱦɥɹ ɢɯ ɪɟɲɟɧɢɹ ɩɪɢɦɟɧɹɸɬɫɹ ɢɡɜɟɫɬɧɵɟ ɚɥɝɨɪɢɬɦɵ, ɢ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɵɣ ɩɨɢɫɤ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɚɧɚɥɢɡɟ ɢ ɫɢɧɬɟɡɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ, ɜ ɨɛɨɛɳɟɧɢɢ, ɤɥɚɫɫɢɮɢɤɚɰɢɢ, ɫɢɫɬɟɦɚɬɢɡɚɰɢɢ ɢɫɫɥɟɞɭɟɦɵɯ ɨɛɴɟɤɬɨɜ ɢ ɜɵɛɨɪɟ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ. ɉɪɢ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɦ ɪɟɲɟɧɢɢ ɬɚɤɨɝɨ ɪɨɞɚ ɡɚɞɚɱ ɮɨɪɦɢɪɭɸɬɫɹ ɥɨɝɢɱɟɫɤɢɟ ɩɪɢɟɦɵ ɦɵɫɥɢɬɟɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ, ɨɜɥɚɞɟɜ ɤɨɬɨɪɵɦɢ, ɦɨɠɧɨ ɫɩɪɚɜɢɬɶɫɹ ɫ ɡɚɞɚɧɢɹɦɢ ɫɥɟɞɭɸɳɟɝɨ ɭɪɨɜɧɹ. Ʉɚɠɞɵɣ ɫɥɟɞɭɸɳɢɣ ɭɪɨɜɟɧɶ ɭɝɥɭɛɥɹɟɬ ɢ ɨɛɨɛɳɚɟɬ ɫɨɞɟɪɠɚɧɢɟ ɩɪɟɞɵɞɭɳɟɝɨ. Ʉ ɡɚɞɚɱɚɦ ɫɪɟɞɧɟɣ ɫɥɨɠɧɨɫɬɢ ɨɬɧɨɫɹɬɫɹ ɧɟɬɢɩɨɜɵɟ ɡɚɞɚɱɢ, ɩɪɢ ɪɟɲɟɧɢɢ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɦɟɧɹɬɶ ɞɟɞɭɤɬɢɜɧɵɟ, ɢɧɞɭɤɬɢɜɧɵɟ ɦɟɬɨɞɵ, ɦɟɬɨɞ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɞɪ. Ʉ ɧɚɢɛɨɥɟɟ ɫɥɨɠɧɵɦ ɨɬɧɨɫɹɬɫɹ ɡɚɞɚɱɢ ɫ ɧɟɩɨɥɧɵɦɢ ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ, ɢ ɬɨɝɞɚ ɩɟɪɜɨɨɱɟɪɟɞɧɵɦ ɞɟɣɫɬɜɢɟɦ ɫɬɚɧɨɜɢɬɫɹ ɪɚɫɲɢɪɟɧɢɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɩɨɥɹ ɡɚɞɚɱɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ ɢɫɯɨɞɧɨɣ ɢɧɮɨɪɦɚɰɢɢ.

Ʌɨɝɢɤɨ-ɩɨɡɧɚɜɚɬɟɥɶɧɵɟ ɡɚɞɚɱɢ ɫɬɢɦɭɥɢɪɭɸɬ ɦɵɲɥɟɧɢɟ ɫɬɭɞɟɧɬɨɜ, ɩɪɢɛɥɢɠɚɸɬ ɢɯ ɭɱɟɛɧɭɸ ɞɟɹɬɟɥɶɧɨɫɬɶ ɤ ɧɚɭɱɧɨɦɭ ɩɨɢɫɤɭ, ɡɧɚɤɨɦɹɬ ɫ ɦɟɬɨɞɚɦɢ ɧɚɭɱɧɨɝɨ ɩɨɡɧɚɧɢɹ ɢ, ɛɟɡɭɫɥɨɜɧɨ, ɝɨɬɨɜɹɬ ɨɛɭɱɚɸɳɢɯɫɹ ɤ ɢɯ ɛɭɞɭɳɟɣ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ. Ɉɧɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɧɚ ɥɟɤɰɢɹɯ, ɫɟɦɢɧɚɪɚɯ, ɩɪɚɤɬɢɱɟɫɤɢɯ ɡɚɧɹɬɢɹɯ ɢ ɤɨɧɫɭɥɶɬɚɰɢɹɯ. ɂɦɟɧɧɨ ɭɱɟɛɧɵɟ ɡɚɞɚɱɢ ɹɜɥɹɸɬɫɹ ɨɞɧɨɣ ɢɡ ɨɫɧɨɜɧɵɯ ɮɨɪɦ ɪɚɡɜɢɬɢɹ ɥɨɝɢɱɟɫɤɨɝɨ ɦɵɲɥɟɧɢɹ ɜ ɨɛɪɚɡɨɜɚɬɟɥɶɧɨɦ ɩɪɨɰɟɫɫɟ.

4

binary digit — ɞɜɨɢɱɧɚɹ ɰɢɮɪɚ). ɋ ɩɨɦɨɳɶɸ ɧɚɛɨɪɚ ɛɢɬɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɥɸɛɨɣ ɫɢɦɜɨɥ: ɱɢɫɥɨ, ɛɭɤɜɭ ɢɥɢ ɡɧɚɤ. Ʉɚɠɞɵɣ ɫɢɦɜɨɥ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɫɶɦɢɪɚɡɪɹɞɧɵɦɢ ɤɨɦɛɢɧɚɰɢɹɦɢ ɛɢɬɨɜ — ɛɚɣɬɚɦɢ (ɬ.ɟ. 1 ɛɚɣɬ = 8 ɛɢɬ), ɩɨɷɬɨɦɭ ɨɫɧɨɜɧɨɣ ɟɞɢɧɢɰɟɣ ɢɡɦɟɪɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɹɜɥɹɟɬɫɹ ɛɚɣɬ. Ɉɞɧɚɤɨ ɤɨɞɢɪɨɜɚɧɢɟ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɦɨɠɟɬ ɛɵɬɶ ɨɱɟɧɶ ɝɪɨɦɨɡɞɤɢɦ. ɉɨɷɬɨɦɭ ɞɥɹ ɡɚɩɢɫɢ ɢ ɯɪɚɧɟɧɢɹ ɡɚɤɨɞɢɪɨɜɚɧɧɨɣ ɞɜɨɢɱɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɦɨɝɭɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɜɨɫɶɦɟɪɢɱɧɚɹ ɢ ɲɟɫɬɧɚɞɰɚɬɟɪɢɱɧɚɹ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ.

1.2.ǷȖȏȐȞȐȖȕȕȣȍ Ȑ ȕȍȗȖȏȐȞȐȖȕȕȣȍ șȐșȚȍȔȣ șȟȐșȓȍȕȐȧ

ɋɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ — ɫɩɨɫɨɛ ɡɚɩɢɫɢ ɱɢɫɟɥ ɩɨɫɪɟɞɫɬɜɨɦ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɧɚɛɨɪɚ ɡɧɚɤɨɜ (ɰɢɮɪ).

Ɉɫɧɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ — ɱɢɫɥɨ ɡɧɚɤɨɜ (ɰɢɮɪ), ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɵɯ ɡɚɩɢɫɵɜɚɸɬɫɹ ɱɢɫɥɚ.

Ⱥɥɮɚɜɢɬ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ — ɧɚɛɨɪ ɡɧɚɤɨɜ.

ȼɫɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɞɜɚ ɤɥɚɫɫɚ: ɧɟɩɨɡɢɰɢɨɧɧɵɟ ɢ ɩɨɡɢɰɢɨɧɧɵɟ.

ȼɧɟɩɨɡɢɰɢɨɧɧɵɯ ɫɢɫɬɟɦɚɯ ɫɱɢɫɥɟɧɢɹ ɧɚ ɡɧɚɱɟɧɢɟ (ɜɟɫ) ɰɢɮɪɵ ɜ ɱɢɫɥɟ ɧɟ ɜɥɢɹɟɬ ɟɟ ɩɨɡɢɰɢɹ ɜ ɡɚɩɢɫɢ ɱɢɫɥɚ.

ɇɚɩɪɢɦɟɪ, ɧɟɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɨɣ ɫɱɢɫɥɟɧɢɹ ɹɜɥɹɟɬɫɹ ɟɞɢɧɢɱɧɚɹ ɫɢɫɬɟɦɚ, ɤɨɬɨɪɚɹ ɢɦɟɥɚ ɯɨɠɞɟɧɢɟ ɟɳɟ ɭ ɩɟɪɜɨɛɵɬɧɵɯ ɥɸɞɟɣ. Ʌɸɛɨɟ ɱɢɫɥɨ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɨɛɪɚɡɭɟɬɫɹ ɩɭɬɟɦ ɩɨɜɬɨɪɟɧɢɹ ɨɞɧɨɝɨ ɡɧɚɤɚ, ɫɢɦɜɨɥɢɡɢɪɭɸɳɟɝɨ ɟɞɢɧɢɰɭ. Ɉɬɝɨɥɨɫɤɢ ɟɞɢɧɢɱɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɜɫɬɪɟɱɚɸɬɫɹ ɢ ɫɟɝɨɞɧɹ (ɫɱɟɬɧɵɟ ɩɚɥɨɱɤɢ ɞɥɹ ɨɛɭɱɟɧɢɹ ɫɱɟɬɭ; ɩɨɥɨɫɤɢ, ɧɚɲɢɬɵɟ ɧɚ ɪɭɤɚɜɚ ɤɭɪɫɚɧɬɨɜ, ɨɡɧɚɱɚɸɳɢɟ ɤɭɪɫ, ɧɚ ɤɨɬɨɪɨɦ ɨɧɢ ɭɱɚɬɫɹ ɢ ɬ.ɩ.).

ȼɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɧɟɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɪɢɦɫɤɭɸ ɫɢɫɬɟɦɭ ɫɱɢɫɥɟɧɢɹ, ɜ ɤɨɬɨɪɨɣ ɜɦɟɫɬɨ ɰɢɮɪ ɢɫɩɨɥɶɡɭɸɬɫɹ ɥɚɬɢɧɫɤɢɟ ɛɭɤɜɵ. ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵ, ɢɥɥɸɫɬɪɢɪɭɸɳɢɟ ɨɛɳɢɟ ɩɪɚɜɢɥɚ ɡɚɩɢɫɢ ɱɢɫɟɥ ɜ ɪɢɦɫɤɨɣ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ

(ɬɚɛɥ. 1.1).

ǺȈȉȓȐȞȈ 1.1

ɐɢɮɪɵ ɜ ɱɢɫɥɟ ɨɛɵɱɧɨ ɡɚɩɢɫɵɜɚɸɬɫɹ ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɜ ɩɨɪɹɞɤɟ ɭɛɵɜɚɧɢɹ, ɩɪɢ ɷɬɨɦ ɧɟɥɶɡɹ ɡɚɩɢɫɵɜɚɬɶ ɪɹɞɨɦ ɛɨɥɟɟ ɬɪɟɯ ɨɞɢɧɚɤɨɜɵɯ

6

ɰɢɮɪ. ȼɟɥɢɱɢɧɚ ɱɢɫɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɫɭɦɦɚ ɢɥɢ ɪɚɡɧɨɫɬɶ ɰɢɮɪ ɜ ɱɢɫɥɟ. ȿɫɥɢ ɦɟɧɶɲɚɹ ɰɢɮɪɚ ɫɬɨɢɬ ɫɩɪɚɜɚ ɨɬ ɛɨɥɶɲɟɣ, ɬɨ ɨɧɚ ɩɪɢɛɚɜɥɹɟɬɫɹ.

ȿɫɥɢ ɦɟɧɶɲɚɹ ɰɢɮɪɚ ɫɬɨɢɬ ɫɥɟɜɚ ɨɬ ɛɨɥɶɲɟɣ, ɬɨ ɨɧɚ ɜɵɱɢɬɚɟɬɫɹ.

ɉɪɢɦɟɪ 3. IX 10 1 .

Ɍɚɤɨɣ ɫɩɨɫɨɛ ɡɚɩɢɫɢ ɱɢɫɟɥ ɩɪɢɜɨɞɢɬ ɤ ɨɱɟɧɶ ɫɥɨɠɧɵɦ ɩɪɚɜɢɥɚɦ ɚɪɢɮɦɟɬɢɤɢ, ɩɨɷɬɨɦɭ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɪɢɦɫɤɚɹ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɧɟ ɩɨ ɩɪɹɦɨɦɭ ɧɚɡɧɚɱɟɧɢɸ, ɧɚɩɪɢɦɟɪ ɩɪɢ ɧɭɦɟɪɚɰɢɢ ɝɥɚɜ ɜ ɥɢɬɟɪɚɬɭɪɧɵɯ ɩɪɨɢɡɜɟɞɟɧɢɹɯ ɢ ɧɚɭɱɧɵɯ ɢɡɞɚɧɢɹɯ, ɜ ɫɟɪɢɣɧɵɯ ɧɨɦɟɪɚɯ ɞɨɤɭɦɟɧɬɨɜ ɢ ɬ.ɩ.

ȼɩɨɡɢɰɢɨɧɧɵɯ ɫɢɫɬɟɦɚɯ ɫɱɢɫɥɟɧɢɹ ɡɧɚɱɟɧɢɟ (ɜɟɫ) ɤɚɠɞɨɣ ɰɢɮɪɵ

ɜɱɢɫɥɟ ɡɚɜɢɫɢɬ ɨɬ ɟɟ ɩɨɡɢɰɢɢ ɜ ɡɚɩɢɫɢ ɱɢɫɥɚ.

Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɡɢɰɢɹ ɰɢɮɪɵ ɜ ɡɚɩɢɫɢ ɱɢɫɥɚ ɧɚɡɵɜɚɟɬɫɹ ɪɚɡɪɹɞɨɦ ɷɬɨɝɨ ɱɢɫɥɚ.

ɉɪɢɦɟɪ 4. Ɋɚɫɫɦɨɬɪɢɦ ɱɢɫɥɨ 7461, ɩɪɟɞɫɬɚɜɥɟɧɧɨɟ ɜ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɟ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɨɧɭɦɟɪɭɟɦ ɪɚɡɪɹɞɵ ɞɚɧɧɨɝɨ ɱɢɫɥɚ. ɇɭɦɟɪɚɰɢɹ ɪɚɡɪɹɞɨɜ ɜ ɰɟɥɵɯ ɱɢɫɥɚɯ ɢɞɟɬ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɧɚɱɢɧɚɹ ɫ ɧɭɥɹ:

7 4 6 1 7 103 4 102 6 101 1 100 .

3 2 1 0

Ɇɵ ɩɨɥɭɱɢɥɢ ɱɢɫɥɨ 7461 ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɚ ɩɨ ɫɬɟɩɟɧɹɦ ɨɫɧɨɜɚɧɢɹ ɞɟɫɹɬɢɱɧɨɣ ɫɢɫɬɟɦɵ (ɬɨɣ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɨɣ ɨɧɨ ɩɪɟɞɫɬɚɜɥɟɧɨ). Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɤɚɠɞɚɹ ɰɢɮɪɚ, ɤɨɬɨɪɚɹ ɜɯɨɞɢɬ ɜ ɡɚɩɢɫɶ ɱɢɫɥɚ 7461, ɨɡɧɚɱɚɟɬ ɨɩɪɟɞɟɥɟɧɧɨɟ ɤɨɥɢɱɟɫɬɜɨ. ȼ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɤɨɥɢɱɟɫɬɜɨ, ɤɨɬɨɪɨɟ ɧɟɫɟɬ ɤɚɠɞɚɹ ɰɢɮɪɚ, ɡɚɜɢɫɢɬ ɨɬ ɟɟ ɩɨɡɢɰɢɢ ɜ ɱɢɫɥɟ.

Ɍɚɤɨɣ ɜɢɞ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɱɢɫɟɥ ɧɚɡɵɜɚɸɬ ɬɚɤɠɟ ɪɚɡɜɟɪɧɭɬɵɦ ɜɢ-

ɞɨɦ.

ɉɪɢɦɟɪ 5. ɉɪɟɞɫɬɚɜɢɦ ɞɟɫɹɬɢɱɧɨɟ ɱɢɫɥɨ 456,92 ɜ ɪɚɡɜɟɪɧɭɬɨɦ ɜɢɞɟ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɨɧɭɦɟɪɭɟɦ ɪɚɡɪɹɞɵ ɞɚɧɧɨɝɨ ɱɢɫɥɚ. ɇɭɦɟɪɚɰɢɹ ɪɚɡɪɹɞɨɜ ɢɞɟɬ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɧɚɱɢɧɚɹ ɫ ɧɭɥɹ — ɞɥɹ ɰɟɥɨɣ ɱɚɫɬɢ ɱɢɫɥɚ, ɢ ɫɥɟɜɚ ɧɚɩɪɚɜɨ — ɞɥɹ ɞɪɨɛɧɨɣ:

4 5 6, 9 2 4 102 5 101 6 100 9 10 1 2 10 2 .

2 1 0 1 2

7

Ɍɟɨɪɟɬɢɱɟɫɤɢ ɫɭɳɟɫɬɜɭɟɬ ɛɟɫɤɨɧɟɱɧɨɟ ɦɧɨɠɟɫɬɜɨ ɩɨɡɢɰɢɨɧɧɵɯ ɫɢɫɬɟɦ ɫɱɢɫɥɟɧɢɹ. ɉɪɢɜɟɞɟɦ ɩɪɢɦɟɪɵ ɫɢɫɬɟɦ ɫɱɢɫɥɟɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦ ɨɫɧɨɜɚɧɢɟɦ (ɬɚɛɥ. 1.2).

ǺȈȉȓȐȞȈ 1.2

ɑɢɫɥɨ ɜ ɥɸɛɨɣ ɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɟɦ q ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɚ ɩɨ ɫɬɟɩɟɧɹɦ ɨɫɧɨɜɚɧɢɹ q. ȼ ɨɛɳɟɦ ɜɢɞɟ ɷɬɨ ɩɪɚɜɢɥɨ ɡɚɩɢɲɟɦ ɬɚɤ:

Xq xn 1 qn 1 xn 2 qn 2 ... x1 q1 x0 q0 ɯ 1 q 1x 2 q 2 ... x k q k ,

ɝɞɟ Xq — ɡɚɩɢɫɶ ɱɢɫɥɚ ɜ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɟɦ q; xi — ɰɢɮɪɵ, ɜɯɨɞɹɳɢɟ ɜ ɡɚɩɢɫɶ ɱɢɫɥɚ (ɜɫɟɝɞɚ ɦɟɧɶɲɟ q); n — ɱɢɫɥɨ ɪɚɡɪɹɞɨɜ ɰɟɥɨɣ ɱɚɫɬɢ;

k — ɱɢɫɥɨ ɪɚɡɪɹɞɨɜ ɞɪɨɛɧɨɣ ɱɚɫɬɢ.

ɉɪɢɦɟɪ 6. ɉɪɟɞɫɬɚɜɢɦ ɱɢɫɥɨ 12101, ɡɚɩɢɫɚɧɧɨɟ ɜ ɬɪɨɢɱɧɨɣ ɫɢɫɬɟɦɟ, ɜ ɜɢɞɟ ɦɧɨɝɨɱɥɟɧɚ ɩɨ ɫɬɟɩɟɧɹɦ ɨɫɧɨɜɚɧɢɹ q=3. ɑɬɨɛɵ ɧɟ ɨɲɢɛɢɬɶɫɹ, ɩɪɨɧɭɦɟɪɭɟɦ ɪɚɡɪɹɞɵ ɱɢɫɥɚ 121013 ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɧɚɱɢɧɚɹ ɫ ɧɭɥɟɜɨɝɨ:

Ɂɚɦɟɱɚɧɢɟ 1. Ɉɫɧɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɱɢɫɥɚ ɨɛɵɱɧɨ ɨɛɨɡɧɚɱɚɟɬɫɹɧɢɠɧɢɦɢɧɞɟɤɫɨɦɢɩɢɲɟɬɫɹɜɫɟɝɞɚɜɞɟɫɹɬɢɱɧɨɣɫɢɫɬɟɦɟ.

ȼɚɠɧɨ, ɱɬɨ ɨɫɧɨɜɚɧɢɟ ɥɸɛɨɣ ɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬ:

•ɧɚɡɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ;

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•ɱɢɫɥɨ ɰɢɮɪ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ;

•ɬɨ, ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ ɜɤɥɚɞ ɰɢɮɪɵ ɜ ɩɨɡɢɰɢɢ ɱɢɫɥɚ ɛɨɥɶɲɟ ɜɤɥɚɞɚ ɬɚɤɨɣ ɠɟ ɰɢɮɪɵ ɜ ɩɪɟɞɵɞɭɳɟɣ ɩɨɡɢɰɢɢ.

ɇɚɩɪɢɦɟɪ, ɜ ɱɢɫɥɟ 55410 ɜɤɥɚɞ ɰɢɮɪɵ 5, ɫɬɨɹɳɟɣ ɜ ɩɟɪɜɨɣ ɩɨɡɢɰɢɢ, ɪɚɜɟɧ 500, ɱɬɨ ɜ 10 ɪɚɡ ɛɨɥɶɲɟ ɜɤɥɚɞɚ, ɤɨɬɨɪɵɣ ɜɧɨɫɢɬ ɰɢɮɪɚ 5, ɫɬɨɹɳɚɹ ɜɨ ɜɬɨɪɨɣ ɩɨɡɢɰɢɢ.

Ⱦɥɹ ɛɨɥɟɟ ɧɚɝɥɹɞɧɨɝɨ ɜɵɹɜɥɟɧɢɹ ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ ɩɨɡɢɰɢɨɧɧɨɣ ɢ ɧɟɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɚɦɢ ɫɱɢɫɥɟɧɢɹ ɪɚɫɫɦɨɬɪɢɦ ɩɪɢɦɟɪ ɫɪɚɜɧɟɧɢɹ ɞɜɭɯ ɱɢɫɟɥ. ȼ ɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɫɪɚɜɧɟɧɢɟ ɞɜɭɯ ɱɢɫɟɥ, ɢɦɟɸɳɢɯ ɨɞɢɧɚɤɨɜɨɟ ɱɢɫɥɨ ɰɢɮɪ, ɩɪɨɜɨɞɢɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɱɢɫɥɚɯ ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɫɪɚɜɧɢɜɚɸɬɫɹ ɰɢɮɪɵ, ɫɬɨɹɳɢɟ ɜ ɨɞɢɧɚɤɨɜɵɯ ɩɨɡɢɰɢɹɯ. Ȼɨɥɶɲɚɹ ɰɢɮɪɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɛɨɥɶɲɟɦɭ ɡɧɚɱɟɧɢɸ ɱɢɫɥɚ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɱɢɫɟɥ 521 ɢ 215 5 ɛɨɥɶɲɟ 2, ɩɨɷɬɨɦɭ ɱɢɫɥɨ 521 ɛɨɥɶɲɟ, ɱɟɦ ɱɢɫɥɨ 215. ȼ ɧɟɩɨɡɢɰɢɨɧɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɷɬɨ ɩɪɚɜɢɥɨ ɧɟ ɞɟɣɫɬɜɭɟɬ. ɉɪɢɦɟɪɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɫɪɚɜɧɟɧɢɟ ɞɜɭɯ ɱɢɫɟɥ IX ɢ VI. ɇɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ I ɦɟɧɶɲɟ, ɱɟɦ V, ɱɢɫɥɨ IX ɛɨɥɶɲɟ, ɱɟɦ ɱɢɫɥɨ VI.

Ⱦɚɥɟɟ ɦɵ ɛɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɬɨɥɶɤɨ ɩɨɡɢɰɢɨɧɧɵɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ.

ɉɪɢɦɟɪ 7. Ʉɚɤɨɟ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɦɨɠɟɬ ɢɦɟɬɶ ɱɢɫɥɨ A32 ? Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɡɚɩɢɫɢ ɞɚɧɧɨɝɨ ɱɢɫɥɚ ɧɟɨɛɯɨɞɢɦɨ ɨɞɢɧɧɚɞɰɚɬɶ ɰɢɮɪ: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, Ⱥ. ɉɨɷɬɨɦɭ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ, ɜ ɤɨɬɨɪɨɣ ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɱɢɫɥɨ A32 , ɞɨɥɠɧɚ ɢɦɟɬɶ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ 11.

ɉɪɢɦɟɪ 8. ɇɚɣɞɟɦ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ, ɟɫɥɢ ɜ ɧɟɣ ɡɚɩɢɫɚɧɵ ɜɫɟ ɫɥɟɞɭɸɳɢɟ ɱɢɫɥɚ: 132, 120, 11, 10101, 2331. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɡɚɩɢɫɢ ɜɫɟɯ ɷɬɢɯ ɱɢɫɟɥ ɧɟɨɛɯɨɞɢɦɨ ɱɟɬɵɪɟ ɰɢɮɪɵ: 0, 1, 2, 3. ɉɨɷɬɨɦɭ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ ɞɨɥɠɧɚ ɢɦɟɬɶ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ 4.

ɉɪɢɦɟɪ 9. ɇɚɣɞɟɦ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ, ɟɫɥɢ ɜ ɧɟɣ ɡɚɩɢɫɚɧɵ ɜɫɟ ɫɥɟɞɭɸɳɢɟ ɱɢɫɥɚ: 732, 2E, 109, 111, 989. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɡɚɩɢɫɢ ɜɫɟɯ ɷɬɢɯ ɱɢɫɟɥ ɧɟɨɛɯɨɞɢɦɨ ɩɹɬɧɚɞɰɚɬɶ ɰɢɮɪ: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E. ɉɨɷɬɨɦɭ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ ɞɨɥɠɧɚ ɢɦɟɬɶ ɦɢɧɢɦɚɥɶɧɨɟ ɨɫɧɨɜɚɧɢɟ 15.

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1.3.ǬȊȖȐȟȕȈȧ, ȊȖșȤȔȍȘȐȟȕȈȧ Ȑ ȠȍșȚȕȈȌȞȈȚȍȘȐȟȕȈȧ șȐșȚȍȔȣ șȟȐșȓȍȕȐȧ

ȼɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ ɧɚ ɗȼɆ ɧɚɢɛɨɥɟɟ ɢɧɬɟɪɟɫɧɵ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɫ ɨɫɧɨɜɚɧɢɹɦɢ 2, 8 ɢ 16. ȼ ɗȼɆ ɩɪɢɦɟɧɹɟɬɫɹ ɞɜɨɢɱɧɚɹ ɫɢɫɬɟɦɚ ɫɱɢɫɥɟɧɢɹ, ɬɚɤ ɤɚɤ ɨɧɚ ɢɦɟɟɬ ɪɹɞ ɩɪɟɢɦɭɳɟɫɬɜ ɩɟɪɟɞ ɞɪɭɝɢɦɢ ɫɢɫɬɟɦɚɦɢ:

• ɫ ɩɨɦɨɳɶɸ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɵ ɫɱɢɫɥɟɧɢɹ ɩɪɨɫɬɨ ɪɟɚɥɢɡɭɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɫɯɟɦɵ ɫ ɞɜɭɦɹ ɭɫɬɨɣɱɢɜɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ (ɟɫɬɶ

ɬɨɤ — 1, ɧɟɬ ɬɨɤɚ — 0);

•ɫɬɚɧɨɜɢɬɫɹ ɜɨɡɦɨɠɧɵɦ ɩɪɢɦɟɧɟɧɢɟ ɚɥɝɟɛɪɵ ɥɨɝɢɤɢ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɥɨɝɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢɧɮɨɪɦɚɰɢɢ (ɜ ɚɥɝɟɛɪɟ ɥɨɝɢ-

ɤɢ ɜɫɟɝɨ ɞɜɚ ɜɨɡɦɨɠɧɵɯ ɪɟɡɭɥɶɬɚɬɚ: ɢɫɬɢɧɚ — 1 ɢ ɥɨɠɶ — 0);

•ɞɜɨɢɱɧɚɹ ɚɪɢɮɦɟɬɢɤɚ ɩɪɨɳɟ ɞɟɫɹɬɢɱɧɨɣ (ɞɜɨɢɱɧɵɟ ɬɚɛɥɢɰɵ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɩɪɟɞɟɥɶɧɨ ɩɪɨɫɬɵ).

Ⱥɪɢɮɦɟɬɢɱɟɫɤɢɟ ɞɟɣɫɬɜɢɹ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɜɵɩɨɥɧɹɸɬɫɹ ɩɨ ɬɟɦ ɠɟ ɩɪɚɜɢɥɚɦ, ɱɬɨ ɢ ɜ ɞɟɫɹɬɢɱɧɨɣ. Ɉɞɧɚɤɨ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɟɞɢɧɢɰɵ ɱɚɳɟ ɩɟɪɟɧɨɫɹɬɫɹ ɜ ɫɬɚɪɲɢɣ ɪɚɡɪɹɞ, ɱɟɦ ɜ ɞɟɫɹɬɢɱɧɨɣ. ȼɨɬ ɤɚɤ ɜɵɝɥɹɞɹɬ ɬɚɛɥɢɰɵ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ (ɬɚɛɥ. 1.3).

Ɂɚɦɟɱɚɧɢɟ 2. ȼ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɫɱɢɫɥɟɧɢɹ ɧɟɬ ɞɪɭɝɢɯ ɰɢɮɪ, ɤɪɨɦɟ 0 ɢ 1, ɩɨɷɬɨɦɭ ɩɪɢ ɫɥɨɠɟɧɢɢ ɞɜɭɯ ɟɞɢɧɢɰ ɩɟɪɟɯɨɞɢɦ ɜ ɫɥɟɞɭɸɳɢɣ, ɫɬɚɪɲɢɣ ɪɚɡɪɹɞ: 1 1 102 (ɧɚɡɵɜɚɟɬɫɹ ɧɟ «ɞɟɫɹɬɶ», ɚ «ɨɞɢɧ

—ɧɨɥɶ», ɬ.ɟ. ɩɟɪɟɱɢɫɥɹɸɬɫɹ ɧɚɡɜɚɧɢɹ ɰɢɮɪ ɫɥɟɜɚ ɧɚɩɪɚɜɨ).

ȼɫɜɹɡɢ ɫ ɬɟɦ, ɱɬɨ ɜ ɞɜɨɢɱɧɨɣ ɫɢɫɬɟɦɟ ɡɚɩɢɫɶ ɱɢɫɥɚ ɞɥɢɧɧɟɟ, ɱɟɦ ɜ ɞɟɫɹɬɢɱɧɨɣ ɩɪɢɦɟɪɧɨ ɜ 3,3 ɪɚɡɚ, ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɜɨɫɩɪɢɹɬɢɹ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ ɛɵɥɨ ɪɟɲɟɧɨ ɪɚɡɛɢɜɚɬɶ ɟɝɨ ɧɚ ɝɪɭɩɩɵ ɪɚɡɪɹɞɨɜ (ɧɚɩɪɢɦɟɪ, ɩɨ ɬɪɢ ɢɥɢ ɱɟɬɵɪɟ ɪɚɡɪɹɞɚ). ɗɬɨ ɨɤɚɡɚɥɨɫɶ ɭɞɚɱɧɵɦ ɪɟɲɟɧɢɟɦ, ɬɚɤ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɢɡ 3 ɛɢɬ ɢɦɟɟɬ 8 ɤɨɦɛɢɧɚɰɢɣ, ɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɢɡ 4 ɛɢɬ — 16. ɑɢɫɥɚ 8 ɢ 16 ɹɜɥɹɸɬɫɹ ɫɬɟɩɟɧɹɦɢ ɞɜɨɣɤɢ, ɩɨɷɬɨ-

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