Напечатали 1.000.000 лотерейных билетов с номерами от 000000 до 999999. билет с номером abcdef считается счастливым, если af+be+cd=100. докажите, что сумма всех счастливых билетов кратна

32/5 = 17/5 1 5/6 = 11/6 3 8/11 = 41/11 1 51/53 = 104/53 2 6/13 = 32/13 7 1/5 = 36/5 5 5/11 = 60/11 6 2/7 = 44/7 3 1/9 = 28/9 7 3/7 = 52/7 17 2/3 = 53/3 5 2/5 = 27/5 3 5/12 = 41/12 29 1/2 = 59/2 7 5/8 = 61/8 9 3/4 = 39/4 11 3/5 = 58/5 13 1/2 = 27/2 3 3/4 = 15/4 2 1/4= 9/4 2 8/9 = 26/9 10 2/3 = 32/3 7 4/5 = 39/5 3 5/6 = 23/6 13 4/9 = 121/9 5 7/8 = 47/8 4 5/7 = 33/7 7/12+3/12 = 10/12 = 5/6 3/7+2/7 = 5/7 13/55-5/55 = 8/55 11/18-7/18 = 4/18 = 2/9 7/10+1/10 = 8/10 = 4/5 15/8-7/8 = 8/8 = 1 12/15+7/15 = 19/15 = 1 4/15 45/100+35/100 = 80/100 = 4/5 65/76-25/76 = 40/76 = 10/19 46/100-41/100 = 5/100 = 1/20 4/5-3/5 = 1/5 4/11+6/1 = 6 4/11 7/8-5/8 = 2/8 = 1/4 77-67/100 = 76 33/100 6/13+7/13 = 13/13 = 1 43/56-33/56 = 10/56 = 5/28 6/23+20/23 = 26/23 = 1 3/23 4/7+2/7 = 6/7 3/4+3/4 = 6/4 = 1 1/2 5/6-1/6 = 4/6 = 2/3 7+1/5 = 7 1/5 3-4/7 = 2 3/7 1-6/11 = 5/11 1+3 5/7 = 4 5/7 8 2/5+3 = 11 2/5 7-4/9 = 2 5/9 8 7/9-6 = 2 7/9 4+1 3/5 = 5 3/5 7-2 1/2 = 4 1/2

32/5 = 17/5 1 5/6 = 11/6 3 8/11 = 41/11 1 51/53 = 104/53 2 6/13 = 32/13 7 1/5 = 36/5 5 5/11 = 60/11 6 2/7 = 44/7 3 1/9 = 28/9 7 3/7 = 52/7 17 2/3 = 53/3 5 2/5 = 27/5 3 5/12 = 41/12 29 1/2 = 59/2 7 5/8 = 61/8 9 3/4 = 39/4 11 3/5 = 58/5 13 1/2 = 27/2 3 3/4 = 15/4 2 1/4= 9/4 2 8/9 = 26/9 10 2/3 = 32/3 7 4/5 = 39/5 3 5/6 = 23/6 13 4/9 = 121/9 5 7/8 = 47/8 4 5/7 = 33/7 7/12+3/12 = 10/12 = 5/6 3/7+2/7 = 5/7 13/55-5/55 = 8/55 11/18-7/18 = 4/18 = 2/9 7/10+1/10 = 8/10 = 4/5 15/8-7/8 = 8/8 = 1 12/15+7/15 = 19/15 = 1 4/15 45/100+35/100 = 80/100 = 4/5 65/76-25/76 = 40/76 = 10/19 46/100-41/100 = 5/100 = 1/20 4/5-3/5 = 1/5 4/11+6/1 = 6 4/11 7/8-5/8 = 2/8 = 1/4 77-67/100 = 76 33/100 6/13+7/13 = 13/13 = 1 43/56-33/56 = 10/56 = 5/28 6/23+20/23 = 26/23 = 1 3/23 4/7+2/7 = 6/7 3/4+3/4 = 6/4 = 1 1/2 5/6-1/6 = 4/6 = 2/3 7+1/5 = 7 1/5 3-4/7 = 2 3/7 1-6/11 = 5/11 1+3 5/7 = 4 5/7 8 2/5+3 = 11 2/5 7-4/9 = 2 5/9 8 7/9-6 = 2 7/9 4+1 3/5 = 5 3/5 7-2 1/2 = 4 1/2