i wants to devide 1 to 81 items worth item1=$1, 2=$2,3=$3......item81=$81 . devide $s between 9 people and everybody should get equal dollars and equal items.
2006-07-19 11:32:24 · 7 answers · asked by kam 1 in Science & Mathematics ➔ Mathematics
The 81 items will cost a total of $3321. (1 + 2 + 3 + ... + 80 + 81)
$3321 divided among 9 people would be $369. As long as you choose 9 items that cost $369, you're good to go.
There are many ways to do this, but one way is to arrange the nine people in a circle around the 81 items, and let the first person pick the most expensive, the 2nd the next most expensive, and so on to the 9th. Once all nine people have chosen one of the nine most expensive items, then repeat the process for the next nine most expensive items except letting the 2nd person choose first. Repeat again for the next group of nine items, letting the 3rd person choose first. Continue this process until everyone has nine items, and everyone has chosen first among any group of nine once.
Person one:
81 + 64 + 56 + 48 + 40 + 32 + 24 + 16 + 8 = 369
Person two:
80 + 72 + 55 + 47 + 39 + 31 + 23 + 15 + 7 = 369
Person three:
79 + 71 + 63 + 46 + 38 + 30 + 22 + 14 + 6 = 369
Person four:
78 + 70 + 62 + 54 + 37 + 29 + 21 + 13 + 5 = 369
Person five:
77 + 69 + 61 + 53 + 45 + 28 + 20 + 12 + 4 = 369
Person six:
76 + 68 + 60 + 52 + 44 + 36 + 19 + 11 + 3 = 369
Person seven:
75 + 67 + 59 + 51 + 43 + 35 + 27 + 10 + 2 = 369
Person eight:
74 + 66 + 58 + 50 + 42 + 34 + 26 + 18 + 1 = 369
Person nine:
73 + 65 + 57 + 49 + 41 + 33 + 25 + 17 + 9 = 369
[Edit] LOL @ Pascal LOL @ Jerome B
2006-07-19 11:59:41 · answer #1 · answered by Anonymous · 4⤊ 1⤋
Give each person the following numbers and each will have 369
1) 81, 10, 19, 28, 37, 2, 55, 64, 73
2) 46, 11, 3, 29, 38, 47, 56, 65, 74
3) 20, 13, 21, 30, 39, 48, 57, 66, 75
4) 4, 12, 22, 31, 40, 49, 68, 67, 76
5) 5, 14, 23, 32, 41, 50, 69, 58, 77
6) 7, 15, 24, 33, 42, 51, 60, 59, 78
7) 9, 16, 26, 35, 18, 53, 62, 71, 79
8) 6, 54, 25, 34, 44, 72, 63, 70, 1
9) 8, 43, 27, 36, 45, 17, 61, 52, 80
2006-07-19 12:16:57 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Total dollars of worth for the items is 81*(81+1)/2 = 3321.
3321/9 = 369, so each person gets $369 worth.
1, 11, 21, 31, 41, 51, 61, 71, 81
2, 12, 22, 32, 42, 52, 62, 72, 73
3, 13, 23, 33, 43, 53, 63, 64, 74,
4, 14, 24, 34, 44, 54, 55, 65, 75
5, 15, 25, 35, 45, 46, 56, 66, 76
6, 16, 26, 36, 37, 47, 57, 67, 77
7, 17, 27, 28, 38, 48, 58, 68, 78
8, 18, 19, 29, 39, 49, 59, 69, 79
9, 10, 20, 30, 40, 50, 60, 70, 80
Each person gets one row of items
To get this chart, I first wrote out the numbers 1-81 in a 9x9 block. Then I read the diagonals. Each row above adds up to $369.
2006-07-19 12:03:44 · answer #3 · answered by Cara B 4 · 0⤊ 0⤋
Distribute the items as follows:
Person 1: 1, 18, 26, 34, 42, 50, 58, 66, 74
Person 2: 2, 10, 27, 35, 43, 51, 59, 67, 75
Person 3: 3, 11, 19, 36, 44, 52, 60, 68, 76
Person 4: 4, 12, 20, 28, 45, 53, 61, 69, 77
Person 5: 5, 13, 21, 29, 37, 54, 62, 70, 78
Person 6: 6, 14, 22, 30, 38, 46, 63, 71, 79
Person 7: 7, 15, 23, 31, 39, 47, 55, 72, 80
Person 8: 8, 16, 24, 32, 40, 48, 56, 64, 81
Person 9: 9, 17, 25, 33, 41, 49, 57, 65, 73
Each person gets 9 items and $369
2006-07-19 11:59:12 · answer #4 · answered by Pascal 7 · 0⤊ 0⤋
$9 and 9 items for each person
2006-07-19 11:42:04 · answer #5 · answered by ? 2 · 0⤊ 0⤋
82*81/2/9=369
1-81+1+71+11+61+21+51+31+41
2-80+2+70+12+60+22+50+33+40
3-79+3+69+13+59+23+49+32+42
4-78+4+68+14+58+24+48+30+45
5-77+5+67+15+57+20+47+29+52
6-76+6+66+16+56+26+46+39+38
7-75+7+65+17+55+27+43+36+44
8-73+8+63+18+54+28+35+37+53
9-74+9+64+19+25+34+62+10+72
2006-07-19 12:24:07 · answer #6 · answered by Poncho Rio 4 · 0⤊ 0⤋
what a neat question
2006-07-19 12:45:28 · answer #7 · answered by snowdrop_crystal 2 · 0⤊ 0⤋