1. ... 2 2. 4 3. ... 5 4. ... 8 5. .......... 10 6. 666.......... 11 7. .......... 12 8. 16 9. 17 10. ......... 19 11. .... 19 12. . 20 13. . 21 14. .. 21

1

: , , , . . , . , . . . , . . , , . , , , . , , . 4 .. , 6 .. . : =1 =10 =100 =2 =20 =200 =3 =30 =300 =4 =40 =400 =5 =50 =500 =60 =600 =7 =70 =700 =8 =80 =800 =9 * 6 F . * 90 & 900 . ( ) ( ) . : 15 (=9 + =5 + =1)=15 23 (=8 + =9 + =5 + =1)=23

2

() 100 1000 . (=3 + =8)=11. 2450 (=200 + =800 + =500 + =100 + =800 + =50)=2450 2500 . =284 (=9 + =5 + =70 + =200)=284 . (=1 + =3 + =10 + =70 + =200)=284 (=1 + =3 + =1 + =9 + =70 + =200)=284 * , ; 430 : =1 =40 =5 =50 =100 =1 =400 =70 =10 =9 =9 =40 =9 =8 =5 =70 =40 =40 =10 =200 =70 =1 =1 430 =200 =300 430 430 =10 =20 =1 430 * ; , . : (=8 + =730 + =15)= 753 (=214 + =8 +=531)= 753 . 3,14 = (338) + (1016) + (940) =2294 (730) =3,14 . , . 3

, , , , ..: =912 =912 =529, =529 =529 , () . .. =780---=781 =773--- =774 . . , ( .1) . (161) + (1263) + (76)= 1500 (=500 + =800 + =200)= 1500 , , . .. , . =905 =905 . =950 =905

. =353 =353

. . . . ( 1 1-5) 4

=373 =1119

=373 3 (3733=1119)

, . ( ). . ( 8 & 16). , . . (373) + (93) = 466 (466) . . 1090= 1090= 1090= . ( ) , . . . (. 23) . , . , , , ( 5-7-8) 1572= + + 1572= 4443= 4443= , ( 3-5) 1878= + + 1879= + + 1880= + ; 5

, , ( 5:6) 1356= + 1356= + (. 1) 902= + 902= 1219= 1219= . 1804= 1804= 1804= ( 15:1) ( ,27) 1380= 1381= 560 .. , , , . . (, , ) , . 587= 587= 2500 . ( ) . , ,

6

. . , , . :

(9+5+70+200) =284 , , . (1+3+1+9+70+200)=284 (1+3+10+70+200)=284 (10+5+100+1=116)+(40+70+50+8=168)=284 . . . (5+20+20+308+200+10+1)=294 (9+5+10+70+200)=294 : . . . . , Lorentz . (70+284+15)=369 (8+361)=369 . (7+5+400+200)=612 (3+100+1+500+8)=612 , ) ; ; () . (4+10+70+200)=284 =284 . , , , , . , . . (10+5+100+5+1+200)=321 (50+1+70+200)=321 7

, . . (1)+(800) 801. ( ) (80+5+100+10+200+300+5+100+1)=801 + (1+800)= 801 . , , , : 99 134 576

809

= 809 (8+801)=809 . . , , . (70+800+50)=920 (70+500+9+1+30+40+70+200)=920 , , . : , , , =(1516) =(1516) =(1516) =(1516) 2846 (284 10)+6 . (500+800+300+70+200+300+5+500+1+50+70+50)=2846 8

: = 140 = 565 = 344 = 1346 = 461 =2856 =2856 . 8 8. (10+8+200+70+400+200) =888 (=1480)= =(1858) (=800)= =(1008) (=1408)= =(1768) (=656)= =(828) (=680)= =(858) (=1880)= =(2358) (=1768)= =(2218) (=644)= =(808+8/2) =888 (226) + (378) + (284) =888 (88) + (800) =800 , . (373) + (515) =888 (25) + (64) + (234) + (515 )=888 : (744) + (144) =888 (515) + (373) =888 ; , . : (200+1+300+1+50+1+200) = 753 (4+100+1+600+40+8) = 753 ;

, .

9

(666) , , , . , . , , . . . . , , , , , , . , . ( ). , , . ( ) , , , . (10+1+80+5+300+70+200) =666 666. ( 1318) 666 (370) + (49) + (247) = 666 6 36 (6 6). 36 : 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+ 21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36=666 ( ) : (4+8+40+8+300+8+100=) 468+ + (20+70+80+8=) 198=666 : (1+5+10)=16 (5+20+30+5+20+300+70+200)=650 (16) + (650) =666 (8) (10+4+5+1)=20 (5+30+30+50)=123 (5+200+300+10)=515 (8) + (20) + (123) + (515) = 666 (80+1+50+1+60+10+50)=322 10

(70+100+3+1+50+70+50)=344 (322) + (344)=666 (1+3+1+9+70+4+70+300+8+200) = 666 (3+5+50+10+20+70+300+8+200) =666 (70+40+1030+8+300+8+200) =666 (5+30+30+8+50+70+80+100+5+80+8+200) =666 ( ) (). (8) + (87) + (571) =666 (70) + (596) =666 . 667 = 667 = 667 = ; , , . : 1.311 (1) + (1310) =1.311 : (370) + (426) + (515) =1.311 ; : 1.310 1.310 1.310 1.310 1.310 1.310 1.310 1.310 1.310 1.310 + 1.310 1.310 1.310

11

. 1.310 : (3+5+50+50+8+300+10+20+70+50) (70+100+3+1+50+70+50) (80+70+50+5+10) (80+1+10+4+10+70+50) 1.310 =566 =344 =175 =225

. (16) + (566) + (344) + (19) + (365) =1.310 : (1) + (50) + (1) + (80) + (1) + (100) + (1) + (3) + (800) + (3) + (70) + (200) =1.310 , , . () 1.310. (20) + (400) + (70) + (500) + (70) + (100) + (10)+ (20) + (70) + (50) = 1.310 , , . , , 1.310. (1) + (100) + (100) + (5) + (2) + (800) + (50) + (10) + (1) + (200) + (400) + (1)=1.310 . , (16) + (565) + (70) + (159) + (31) + (8) + (461) = 1310= =1310 . . : (370) + (355) + (370) + (215)= 1310 (395) + (915)= 1310 10 ( ), : (131) 10= 1310 (55) + (76) = (131) 10 = 1310 12

: (8) + (1111) + (25) + (166)= 1310 . , , 406 46 4 = 46 = 406 . 452= (46) + (406) 453= 454= ( ) . ( ) ( ), . . ( ). . . ... ... , : 671= 672= (294) + (378) . , . , . 432= (378) + (54) 433= (300+5+40+80+8) 19 , , . , ... . 13

384= 385= ( ). ... ... ( 14-639) . , ( ) . 588= 589= 590= ; . (466) + (123)= 589 ; , . , . , . , ... . : ... , , , . , ... ... (, 23) . . , 1981 . 700.000 . 25.000 . , , 100.000 800.000 , , 14

, 15.000 ..

368.000 , . 123. (5) + (30) + (30) + (8) + (50) = 123 , , . , , . , , . , , , , , . , 266 (5) + (30) + (30) + (1) + (200) = 266 * : * (131) (135) (266): (80) + (1) + (50) =131 +(4) + (70) + (60) + (1) =135 =266 () 1234. (3) + (30) + (800) + (200) + (200) + (1) =1234 1,2,3,4 , , , , 15

. : (266) + (1234) = 1500 ... (500) + (800) + (200)= 1500 ; . . . 4 437 955 508 361 1.441 515 770 4.995 370 1.090 1.150 1.820 565 4.995

8 456 1.150 , 2.083 , . 515 783 4.995

, , . . + (6) 3.999 1+2+3+4+5+6+7+8+9+10+20+30+40+50+60+70+80+90+100+200+300+400 +500+600+700+800 = 3.999 16

... , : 8 1.41 0 15 508 2.05 =3.999 8

; (8) + (1263) = 1271 (565) + (1) + (705)= 1.271 . ... . , . ; ; 1.500= 1.500= 1.500= (266) + (1234) , 12 , 6 (. ), 6 . / ( ), , . 666= . . () . 699= 699= 699= . 17

( ) . , . (4+10+20+1+10+70+200+400+50+8) = 773 (4+10+20+1+200+300+8+100+10+70+50) = 773 (80+1+50+300+70+5+9+50+8+200) =773 : (70+4+10+20+1+10+70+200) = 385 ... (10+5+100+7+200) = 385 . ;

, : : =834 =834 =834 =834 =834 =834 , , , , . , , , - , , , - .

18

() , .

, , . . , 78 (1+2+3+4+5+6+7+8+9+10+11+12=78) 78, 10 ( ) 78 10 = 780. 780 =(2+100+70+600+8)=780 780 =(5+4+1+500+70+200)=780 ... 780 =(200+10+300+70+200)=780 , , , , . ... (780) (8+100+1)=109 (671). = (1+100+300+70+200) = 761 78 780 6 (7+8)=15 (1+5)=6 . 212.. : = 48 = 510 = 970 (40+8) (40+70+400) (300+70+400+200) 19

=1.140 =1.007 =3.675 (20+400+20+30+70+400+200) (300+1+100+1+300+300+5)

:

= 141 = 515 = 940 =2.079 =3.675

(1+2+5+2+1+1070+50) (5+200+300+10) (20+400+20+30+70+400)(300+5+300+100+1+3+800+50+10+200+40+70+200)

= 3675 = 3675 ( ) . , . Lindemann 1882 , . ( ) (69-125 ..) , , . . =1005 (75) + (454) + (476) = 1005 . . ;

20

1. ...... 24 ...... 24 6........ 24 2. ................................ 25 3. / ........................ 28 ....... 28 4. ........ 5. ........ ............ 6. ........ 26 ....... 7. ..........

21

/ () . / , : : =55 >(5+5)= 10>(1+0)=1 1. =532 > (5+3+2)=10 >(1+0)=1 1. =1288 > (1+2+8+8) =19 > (1+9)=10 > (1+0)=1 1. , , . . 6 : 6 (, , , 6, ) 6 (, , , . ). 12, 6 ( ). 6 ( ) : : (78) (7+8)= 15= (1+5) =6 = (123) 1+2+3=6 =(141) 1+4+1 = 6 (2121) 2+1+2+1= 6 + (2121) 2+1+2+1-6 (1500) 1+5+0+0 = 6 (213) 2+1+3 = 6 (600) 6+0+0 = 6 (15) 1 +5 = 6 (60) 6+0 =6 6 ()

24 () 6 , 6 , 6 6 . 22

**

1908 , 17 . .. = 1281 ' =1281 ( ) . =595 =595 ' , . . - ( ).

(500 + 1 + 200 + 300 + 70 + 200)= 1281 (80+400+100+1+400+30+70+200) = 1281 , . . (504) + (1481)= 1985 (576) + (894) + (515) = 1985 - ( ). ** ( ) ,

23

, . , , . , . , , . (23.960 ..). , . , . . , . , . , . , , , , , , ... , ... . , . 24

. , , . . , . , ... . , (. 224) = , , . (. 12) = , . , , . (. 346) = , , : , , ... (. 314) = . , , . , , , , , , , . (. 227) = , . , . (. 209) = . , . . (. ) . . (. 592) = . . , , , . : , , , . (. 146) = . . : , , , . (. 825) = . : , , , , , , , . (. 92) = . : , , , , , , , . = . : ( ), ( ), ( ), ( ). = , ( ). = . , .

25

, , , . : = . . () , . , , . , , . , , , , , , . . ... , , 1998 .

. ... , ..., ... ( 6) A= B= C= D= E= F= G= 6 12 18 24 30 36 42 H= I= J= K= L= M= N= 48 54 60 66 72 78 84 O= P= Q= R= S= T= U= 90 96 102 108 114 120 126 V= W= X= Y= Z= 132 138 144 150 156

26

: COMPUTER (18+90+78+96+126+120+30+108) = 666 , . HUMANITY (48+126+78+6+84+54+120+150) = 666 ... ... NEW YORK (84+30+138+150+90+108+66) = 666 ( ) . ( ) 2003 : ) Hellenic Quest CNN . , ) , ) . , , . ) , , (, , ), , ) (.. + ). , , ) , , ) , . , , .. : , 21 2003 e-mail. 27

. . . / (50)

28