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High School Time Capsule ?

High School Time Capsule.?
I just started high school (Grade 8) and our counselor is doing a project with us. A time capsule that we will all open before the graduation ceremony (5 years) What do you think i should put in it?
I've already got:

A mix cd i made of my fav music
Stamps
a bracelet my friend made me
a few pennies for good luck
a 50 cent coin
a sea shell my friend painted me
a few beads from my little sisters lucky bracelet
a few googley eyes (inside thing)
a rock i got from my teacher in gr 1 (inside thing)
"oh the places you'll go!" Poem my grade 7 teacher printed out for us for elementary school grad
business cards and flyer card things from my moms business
grade 8 schedule
piece of paper with my student number on it for the first time i forgot it
my first excused absence note
school store money that i won from the grade 8 scavenger hunt
list of my likes and dislikes
a letter poem from my friend
a drawing i made
pictures of my friends and family
magazine clippings
news paper clippings
a twilight poster
taxi reciepts
a letter from my little sister
a letter from my olderest cousin (gr. 11 going to be first to graduate high school, ill be either second or third depending on someone in my family, im really not sure about him) shes also including a few things but she wont let me see what they are
letter from my mom
letter i wrote to myself

the capsule is a nice but small chest looking wooden box (not bigger then a shoe box)

What else should i put? I want a lot of things in there, it makes it more exciting to open!

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logo High School Time Capsule ?
NICE 1904 Indian Head Penny A Good Coin FREE SHIPPING
NICE 1904 Indian Head Penny A Good Coin FREE SHIPPING
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1903 INDIAN HEAD CENT PENNY A5357 A GOOD COIN
1903 INDIAN HEAD CENT PENNY A5357 A GOOD COIN
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1951 S Lincoln Wheat 1 Cent Penny Nice Coin
1951 S Lincoln Wheat 1 Cent Penny Nice Coin
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Money Changing Problem Proof (complex)?

The Money Changing Problem (for my purposes) is to find the smallest number of coins needed to get some dollar value. The "greedy algorithm" is the one where we repeatedly take the largest possible coin without exceeding our limit.

Example: To make 73 cents,
Take a quarter (25)
Take a quarter (50)
Take a dime (60)
Take a dime (70)
Take a penny 3x (73)

The greedy algorithm always works with US denominations, but may not with others.

For example, with coins 1, 5, 10, 20, 25, if we want to get 40, we would take 25, then 10, then 5, but the optimal solution is to take 20 and 20 (two coins instead of three).

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Now, on to my question:

Suppose the denominations are powers of a fixed integer p > 1 (that is, the denominations are 1, p, p^2, ... , p^m) for some fixed integer m). Prove or disprove that the greedy algorithm above correctly solves the Money Changing Problem for these denominations (if we apply the algorithm, it always gives us the fewest number of coins).

-----------

My gut tells me that it is true, but I am having trouble proving it. Any help would be appreciated.

Thanks!

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logo Money Changing Problem Proof (complex)?
19 Indian head pennies all different
19 Indian head pennies all different
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Unsearched Penny Roll 11 IH Reverse showing on Both ends
Unsearched Penny Roll 11 IH Reverse showing on Both ends
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Indian Head Cent Collection 1859 1907 Mixed Grades 125 Coins No Reserve
Indian Head Cent Collection 1859 1907 Mixed Grades 125 Coins No Reserve
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1983 D D Lincoln Cent US Coins
1983 D D Lincoln Cent US Coins
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1860 INDIAN HEAD CENT COPPERNICKEL fn301
1860 INDIAN HEAD CENT COPPERNICKEL fn301
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1862 INDIAN HEAD CENT COPPERNICKEL FULL LIBERTY fn302
1862 INDIAN HEAD CENT COPPERNICKEL FULL LIBERTY fn302
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“OUR hearts may condemn us.” With those words, the Bible acknowledges that at times our heart may cause us to be overly critical of ourselves. Indeed, it may insist that we are unworthy of God’s love and care. Yet, the Bible reassures us: “God is greater than our hearts and knows all things.” (1 John 3:19, 20) God knows us better than we know ourselves. His view of us may be very different from the way we view ourselves. What, then, are we worth in the eyes of the one who really matters—Jehovah God? The answer can be found in a touching illustration that Jesus used on two separate occasions.

On one occasion, Jesus said that “two sparrows sell for a coin of small value.” (Matthew 10:29, 31) According to Luke 12:6, 7, Jesus pharmacies online also said: “Five sparrows sell for two coins of small value, do they not? Yet not one of them goes forgotten before God. . . . Have no fear; you are worth more than many sparrows.” This simple but powerful illustration teaches us how Jehovah views each of his worshippers.

Sparrows were among the cheapest of all birds used for food. Jesus had no doubt observed poor women—perhaps even his own mother—in the marketplace buying these tiny birds to feed their family. For one assarion, a coin worth less than five cents in modern values, a buyer could purchase two sparrows. These birds were so inexpensive that for two coins, the buyer received not four but five sparrows, an extra one being included at no additional charge.

Jesus explained that not a single sparrow “goes forgotten before God” or falls “to the ground without” the Father’s knowledge. (Matthew 10:29) Jehovah notices each time a sparrow falls to the earth perhaps because it is injured or alights on the ground in search of food. The seemingly insignificant birds that were not too little for Jehovah to create are not too little for him to remember. In fact, he values them, for they are precious living things. Do you see the point of Jesus’ illustration?
In his teaching, Jesus often used contrasts, reasoning from the lesser to the greater. For example, Jesus also said: “Ravens neither sow seed nor reap, and they have neither barn nor storehouse, and yet God feeds them. Of how much more worth are you than birds?” (Luke 12:24) Now the point of Jesus’ words about the sparrows becomes clear: If Jehovah cares for these tiny birds, how much more will he care for humans who love and worship him!

In light of Jesus’ words, we need not feel that we are too unworthy to be noticed and cared for by the God who “is greater than our hearts.” Is it not comforting to know that our Creator may see in us what we may be unable to see in ourselves?
w 08 4/1 pg9

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logo Many on this forum have painted God as hardhearted. How can you read this and feel He is hardhearted?
5 Old Window Wrap Wheat Rolls Unsearched
5 Old Window Wrap Wheat Rolls Unsearched
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1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
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1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
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it says one cent on the back and has a small s under the 1947. I was curious as to whether this is something a Buy Acomplia Online Without Prescription collector would want, and how much it is "worth". If you answer that it is worth one cent, you are unfunny, unoriginal, and lame. Good day to all and thank you.

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logo Hello coin collectors, I have a 1947 us penny?
5 Old Window Wrap Wheat Rolls Unsearched
5 Old Window Wrap Wheat Rolls Unsearched
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1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
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1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
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Incredible Antique 25¢ Roll wrapped Steel Strong Double Wheat Mystery Ends
Incredible Antique 25¢ Roll wrapped Steel Strong Double Wheat Mystery Ends
Paypal   US $3.25
1909 VDB S 1909 P in Antique 25¢ Trentwood Half Roll of Teen Prior m
1909 VDB S 1909 P in Antique 25¢ Trentwood Half Roll of Teen Prior m
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OLD US COINS 1858 RARE FLYING EAGLE CENT PRE CIVIL WAR
OLD US COINS 1858 RARE FLYING EAGLE CENT PRE CIVIL WAR
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When I first got him three weeks ago, a week after i got him he has a small sport of wet fur but I thought maybe he just was grooming himself, it never seemed to be a problem. But now it looks horrible, it seems to have fur missing and the spot is about the size of a US 5 cent coin and it's wet. He also seems sick:

http://answers.yahoo.com/question/index;_ylt=AqkDks1tfhz1DkLgWcbzBwDsy6IX;_ylv=3?qid=20100420161727AACOPnJ

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logo My hamster has a big spot on his side with some fur missing and its wet?
5 Old Window Wrap Wheat Rolls Unsearched
5 Old Window Wrap Wheat Rolls Unsearched
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1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
1862 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9385
Paypal   US $3.36
1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
1859 INDIAN HEAD CIVIL WAR ERA COPPER NICKLE WHITE CENT 9361
Paypal   US $2.05
Incredible Antique 25¢ Roll wrapped Steel Strong Double Wheat Mystery Ends
Incredible Antique 25¢ Roll wrapped Steel Strong Double Wheat Mystery Ends
Paypal   US $3.25
1909 VDB S 1909 P in Antique 25¢ Trentwood Half Roll of Teen Prior m
1909 VDB S 1909 P in Antique 25¢ Trentwood Half Roll of Teen Prior m
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OLD US COINS 1858 RARE FLYING EAGLE CENT PRE CIVIL WAR
OLD US COINS 1858 RARE FLYING EAGLE CENT PRE CIVIL WAR
Paypal   US $11.50

Click on the Dollar and Cents brochure site. In this site are three other sites, Types of US Generic Cialis paper money, Circulation of money and spotting counterfeit currency that can be used to answer the following questions. What are the denominations of Federal Reserve notes being printed? What was the largest denomination Federal Reserve Note ever printed and circulated, and when was it last printed? When as the last lilver dollar minted? What have been the largest and smallest US coin denominations since the Coinage Act of 1792?

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logo Visit the web site for the Federal Reserve Bank in Atlanta @ www.frbaltanta.org?
19 Indian head pennies all different
19 Indian head pennies all different
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Unsearched Penny Roll 11 IH Reverse showing on Both ends
Unsearched Penny Roll 11 IH Reverse showing on Both ends
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Indian Head Cent Collection 1859 1907 Mixed Grades 125 Coins No Reserve
Indian Head Cent Collection 1859 1907 Mixed Grades 125 Coins No Reserve
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One coin is online meds without prescription a US 1884, dollar (coin).

I have two US 50 cent pieces. One is 1834, the other is 1825. Both have a tiny hole that looks like it was drilled to wear as a necklace but the hole is so tiny I can't imagine a chain made that small! The holes are like pin holes. Very tiny.

Are they worth my time in selling them and how would I go about doing that?

 


logo I have some coins from 1800s. Are they worth much?
2011 P D Lincoln SHIELD Cents PCGS MS66RD 2 Coin Set
2011 P D Lincoln SHIELD Cents PCGS MS66RD 2 Coin Set
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SCRUFFY 1943 S WW II Mint Era LINCOLN WHEAT STEEL WAR PENNY Grandfathers Estate
SCRUFFY 1943 S WW II Mint Era LINCOLN WHEAT STEEL WAR PENNY Grandfathers Estate
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NICE 1904 Indian Head Penny A Good Coin FREE SHIPPING
NICE 1904 Indian Head Penny A Good Coin FREE SHIPPING
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1903 INDIAN HEAD CENT PENNY A5357 A GOOD COIN
1903 INDIAN HEAD CENT PENNY A5357 A GOOD COIN
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1951 S Lincoln Wheat 1 Cent Penny Nice Coin
1951 S Lincoln Wheat 1 Cent Penny Nice Coin
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1955 D Lincoln Wheat 1 Cent Penny Nice Coin
1955 D Lincoln Wheat 1 Cent Penny Nice Coin
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