How many coins left? In my purse I had some pennies, dimes, and Sacagawea dollar coins, total 16 coins…?
In my purse I had some pennies, some dimes, and some Sacagawea dollar coins, total 16 coins. And I went to a candy store, and I saw that all candies were equally priced. Altogether they had 36 varieties of candies, and picked one candy of each variety, and paid with my coins.
How many coins left?
I’m assuming you had exact change to pay for the candy.
This is actually an interesting problem in mod arithmetic. The numbers 1, 10, 100 (corresponding to penny, dime, and dollar) all equal 1 in mod 9. So, with 16 coins, the mod 9 total of your coins is 7.
Now, 36 = 0 mod 9. So after buying the candy, the coins in your pocket will still total 7 mod 9. Since you can’t still have 16 coins, the number left is 7, as this is the only number less than 16 which is 7 mod 9 .
2000 Sacagawea Dollar Coin
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| | 2009 P&D Type A AND B Sacagawea Dollars 4 Coins SATIN $16.45 |
| | 2002 P&D BU Mint State Sacagawea US Dollar (2 Coins ) $5.90 |
| | 2010-S Proof Deep Cameo Sacagawea US One Dollar Coin $5.95 |
| | Sacagawea Nation American Dollar Coin 2010 D $1.99 |
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| | 2001 p&d US MINT UNCIRCULATED 20 COIN SET – 2nd YEAR ISSUE of SACAGAWEA DOLLAR$ $9.00 |
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| | 2000-2011 P & D 25-COIN UNCIRCULATED SACAGAWEA DOLLAR SET WITH BOOKS! $74.95 |
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| | SACAGAWEA PROOF DOLLAR LOT – 13 DIFFERENT YEAR COINS IN TOTAL – 2000-2012 $39.95 |
| | 2000-2011 Sacagawea PCGS Dollar Set 12 Coins Total $140.00 |
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| | 2011 S PCGS PR69 FIRST STRIKE PRESIDENT, 4 COINS & 2011 SACAGAWEA PCGS PR69 $29.99 |
