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Wednesday, 27 july 2016 |
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Numarul suficient de greutati |
Proposed by
Gabi |
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| (2 comments) | 1.795 times displayed |
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Care este numarul suficient de greutati (exprimate in kilograme - numere intregi) diferite intre ele necesare pentru a putea cantari orice numar intreg de kilograme intre 1 si 40, folosind o singura balanta?
Si, daca nu cer prea mult, care ar fi aceste greutati? Cate kg ar avea fiecare ? |
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Sunt suficiente urmatoarele greutati: 1, 3, 9, 27 kg.
Tabelul de mai jos exprima cum trebuie asezate greutatile pe balanta pentru a se putea cantari orice obiect intre 1 si 40 kg:
| Greutatea
obiectului
|
Talerul liber |
Talerul cu obiectul |
| 1 |
1 |
|
| 2 |
3 |
1 |
| 3 |
3 |
|
| 4 |
1+3 |
|
| 5 |
9 |
1+3 |
| 6 |
9 |
3 |
| 7 |
1+9 |
3 |
| 8 |
9 |
1 |
| 9 |
9 |
|
| 10 |
1+9 |
|
| 11 |
3+9 |
1 |
| 12 |
3+9 |
|
| 13 |
1+3+9 |
|
| 14 |
27 |
1+3+9 |
| 15 |
27 |
3+9 |
| 16 |
1+27 |
3+9 |
| 17 |
27 |
1+9 |
| 18 |
27 |
9 |
| 19 |
1+27 |
9 |
| 20 |
3+27 |
1+9 |
| 21 |
3+27 |
9 |
| 22 |
1+3+27 |
9 |
| 23 |
27 |
1+3 |
| 24 |
27 |
3 |
| 25 |
1+27 |
3 |
| 26 |
27 |
1 |
| 27 |
27 |
|
| 28 |
1+27 |
|
| 29 |
3+27 |
1 |
| 30 |
3+27 |
|
| 31 |
1+3+27 |
|
| 32 |
9+27 |
1+3 |
| 33 |
9+27 |
3 |
| 34 |
1+9+27 |
3 |
| 35 |
9+27 |
1 |
| 36 |
9+27 |
|
| 37 |
1+9+27 |
|
| 38 |
3+9+27 |
1 |
| 39 |
3+9+27 |
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| 40 |
1+3+9+27 |
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Tags:
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problema zilei,
probleme de matematica,
amuzante,
matematica amuzanta,
cantarire,
balanta,
greutati,
kg
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