How many possible values can there be for three coins selected from among pennies, nickels, dimes, and quarters?
2006-09-29 05:19:00 · 16 answers · asked by Sasha 2 in Science & Mathematics ➔ Mathematics
yes, 20 is the correct answer. I wrote a program to verify. There are 4^3 = 64 possibilities, but 44 of them have the same numerical value. For example, (penny, penny, quarter) is the same as (quarter, penny, penny). Nobody posted an elegant solution but AmarSingh was the closest.
2006-09-29 05:27:59 · answer #1 · answered by Joe C 3 · 0⤊ 0⤋
There are 20 possible values
1. P + P + P / 1 + 1 + 1 = 3
2. P + P + N / 1 + 1 + 5 = 7
3. P + N + N / 1 + 5 + 5 = 11
4. P + P + D / 1 + 1 + 10 = 12
5. N + N + N / 5 + 5 + 5 = 15
6. P + N + D / 1 + 5 + 10 = 16
7. N + D + N / 5 + 10 + 5 =20
8. P + D + D / 1 + 10 + 10 = 21
9. N + D + D / 5 + 10 + 10 =25
10. P + P + Q / 1 + 1 + 25 = 27
11. D + D + D / 10 + 10 + 10 = 30
12. P + N + Q / 1 + 5 + 25 = 31
13. N + Q + N / 5 + 25 + 5 = 35
14. P + D + Q / 1 + 10 + 25 = 36
15. N + Q + D / 5 + 25 + 10 = 40
16. D + D + Q / 10 + 10 + 25 = 45
17. P + Q + Q / 1 + 25 + 25 = 51
18. N + Q + Q / 5 + 25 + 25 = 55
19. D + Q + Q / 10 + 25 + 25 =60
20. Q + Q + Q / 25 + 25 + 25 = 75
2006-09-29 06:35:06 · answer #2 · answered by tiggergoesbouncebounce 2 · 0⤊ 0⤋
20 different sums
Coin Coin Coin Sum
1 1 1 3
1 1 5 7
1 5 1 7
5 1 1 7
1 5 5 11
5 1 5 11
5 5 1 11
1 1 10 12
1 10 1 12
10 1 1 12
5 5 5 15
1 5 10 16
1 10 5 16
5 1 10 16
5 10 1 16
10 1 5 16
10 5 1 16
5 5 10 20
5 10 5 20
10 5 5 20
1 10 10 21
10 1 10 21
10 10 1 21
5 10 10 25
10 5 10 25
10 10 5 25
1 1 25 27
1 25 1 27
25 1 1 27
10 10 10 30
1 5 25 31
1 25 5 31
5 1 25 31
5 25 1 31
25 1 5 31
25 5 1 31
5 52 5 35
5 25 5 35
25 5 5 35
1 10 25 36
1 25 10 36
10 12 5 36
10 25 1 36
25 1 10 36
25 10 1 36
5 10 25 40
5 25 10 40
10 5 25 40
10 25 5 40
25 5 10 40
25 10 5 40
10 10 25 45
10 25 10 45
25 10 10 45
1 25 25 51
25 1 25 51
25 25 1 51
5 25 25 55
25 5 25 55
25 25 5 55
10 25 25 60
25 10 25 60
25 25 10 60
25 25 25 75
2006-09-29 05:33:17 · answer #3 · answered by DanE 7 · 1⤊ 0⤋
1 1 1 = 3 5 5 5 = 15
1 1 5 = 7 5 5 10 = 20
1 1 10 = 12 5 5 25 = 35
1 1 25 = 27 5 10 10 = 25
1 5 5 = 11 5 10 25 = 40
1 5 10 = 16 5 25 25 = 55
1 5 25 = 31 10 10 10 = 30
1 10 10 = 21 10 10 25 = 45
1 10 25 = 36 10 25 25 = 60
1 25 25 = 51 25 25 25 = 75
2006-09-29 05:35:06 · answer #4 · answered by bob h 3 · 0⤊ 1⤋
20
2006-09-29 05:35:13 · answer #5 · answered by T 5 · 0⤊ 0⤋
You have four choices for the first coin. Then 3 for the second coin and 2 for the final coin. 4*3*2=24. that gives you 24 possible combinations of coins to choose from. However, this would result in the same coins being chosen just in differnt order. So to determine this answer make a simple chart of coins and determine that each coin has three possible combinations it can be a part of and one that it will not be part of. So there are 4 different values $0.26, $0.31, $0.36, and $0.40.
2006-09-29 05:33:58 · answer #6 · answered by spc_rice 2 · 0⤊ 1⤋
4^3=64
2006-09-29 06:09:45 · answer #7 · answered by phaleg 2 · 0⤊ 1⤋
Possible values
1)=1Pennie+1nickle +1dime=$0.16 when all different
2)=1Pennie+1nickle +1quarter=$0.31when all different
3)=1Pennie+1dime+1 quarter=$0.36 when all different
4)=1 nickle+1dime+1quarter =$0.40when all different
When two are of same type
5)=2 nickle+1Pennie=$0.11
6)=2 nickle+1dime=$0.20
7)=2 nickle+1quarter=$0.35
8)=2 pennies+1nickle=$0.07
9)=2 pennies+1dime=$0.12
10)=2 pennies+1quarter=$0.27
11)=2 dimes+1pennies=$0.21
12)=2 dimes+1nickle=$0.25
13)=2 dimes+1qua tr=$0.4511)
14)=2 quarters+1pennies=$0.51
15)=2 quarters +1nickle=$0.55
16)=2 quarters+1 dime=$0.60
Similarly when three are of same type coin
17) 3 pennies =$0.03
18) 3 nickles= $0.15
19) 3 dimes = $0.30
20) 3 quarters = $0.75
2006-09-29 05:58:45 · answer #8 · answered by Amar Soni 7 · 1⤊ 0⤋
4 x 4 x 4 = 64
2006-09-29 05:26:37 · answer #9 · answered by treseuropean 6 · 0⤊ 2⤋
ok, there are 3 8 hour shifts in the process the day and no elf is authorized to paintings better than one shift. If there are 9,000 elves engaged on an identical time, this means they are all area of an identical shift, superb? If it rather is genuine than those 9,000 elves would be unable to paintings back for something of the day because of the fact they are basically required one shift. So if there are 3 shifts and 9,000 are continually engaged on an identical time, you will possibly mulitply 9,000 by potential of three to get the completed style of elves working on a daily basis: 27,000 elves. Now if each and every elf desires cookies for the time of his smash, you in simple terms multiply 27,000 by potential of two: fifty 4,000 cookies. So very final solutions: 27,000 individual elves paintings on a daily basis. fifty 4,000 cookies are needed on a daily basis
2016-10-15 08:29:08 · answer #10 · answered by seelye 4 · 0⤊ 0⤋