Ese BIO 27/10 - soluzioni

1. 4^5 = 2^(10) = 1024

2. 7*6*5 = 210

3. (100 3) = 161700

4. 6! = 720;	10!/2 = 1814400 

5. (7 3) = 35

6. (6 1) + (6 2) + (6 3) + (6 4) + (6 5) = 2^6-2 = 62

7. (52 7) = 133784560
(13 3)*(13 4) = 286*715 = 204490
(48 3) = 9776

8. Simultanea:
di 3:	4
di 6:	6
di 7:	6
di 15:	1
Successiva:
di 3:	2^3 = 8
di 6:	2^6 - 1 = 63
di 7:	2^7 - 1 - 7 = 120
di 15:	(15 5) = 3003

9. (7 2) - 6 = 15
(89 2) = 3916
(45 2) * 45 = 2047
(79 4) = 1502501
(90 2) - (45 2) = 3015
5 * 3 * 2 = 30
(8 2) - 12 = 16 = 6 * 2 + 8 / 2
9! / (2! * 3! * 4!) = 1260 = (9 2) * (7 3) 
3R,1G + 3R,1B + 2R,2G + 2R,1G,1B + 2R,2B + 1R,2G,1B + 1R,1G,2B + 1R,3B + 2G,2B + 1G,3B + 4B
4     + 4     + 6     + 12       + 6     + 12       + 12       + 4     + 6     + 4     + 1  = 71
100000 - 10 = 99990
100000 - 10 - 10 * 10 * (5 1) - 10 * 10 * (5 2) = 998490
(100 3) + 50 * (50 2) = 222950
(5 2) * 11 * 10 * 9 = 9900

10. 1/(90 3) = 1/117480

11. 5/(7 3) =  1/7

12. ((31+30)/365)^6

13. ((4 2) + (8 2)) / (12 2) = 17/33

14. 
(10 2) * (8 4) / (12 4) * (8 4) = 1/11
(10 3) * (8 4) / (12 4) * (8 4) = 8/33
3/11

15. x:y=4:3, x+y=14, x=8, y=6
(20 8) * (15 6) = 630479850
(19 7) / (20 8) = (14 5) / (15 6)

(5k-1 2k-1)/(5k 2k) = 5/2
(n*k-1 p*k-1)/(n*k p*k) = p/n

16. ( (4 2) + (8 2) + (10 2) + (2 2) ) / (24 2) = 20/69

17. 
10 * (7 3) * 9 * 8 * 7 * 6 = 1058400
9 * 8 * 7 * 6 = 3024
9 * 8 * 7 * 6 / 10 * (7 3) * 9 * 8 * 7 * 6 = 1/350
5 * 9 * 8 * 7 * 6 / 10 * (7 3) * 9 * 8 * 7 * 6 = 1/70

18.
1 / 7 * 6 * 3! = 1 / 252
1 / 252 * 0 + 251 / 252 * 1 / 251 = 1 / 252

19. 
(12 3) * (8 6) = 6160
n:b=3:2, n+b=10, n=6, b=4
(12 6) * (8 4) = 64680
(10 4) * (5 1) / 64680 = 5/308

20.
21 * (6 3) * 20 * 19 * 18 = 2872800
1 / 21 * (6 3) = 1/420

21.
25^4
(4/25)^4, (21/25)^4
(4 2) * (4/25)^2 * (21/25)^2