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I have never had modular arithmetic, but if mod is just taken as remainder it can easily be seen that 2^1001mod33 will be 2 and 2-2=0.
Calculate this~!MUST be solved in your head!
155 Replies - 13378 Views - Last Post: 04 May 2009 - 08:17 PM
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#108
BigAnt
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Re: Calculate this~!
Posted 19 January 2009 - 09:33 PM
Well when we wait to verify the solution or not lets try this:
The Puzzle: The following equation is wrong: 101 - 102 = 1
Move one numeral to make it correct.
The Puzzle: The following equation is wrong: 101 - 102 = 1
Move one numeral to make it correct.
#109
Gloin
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Re: Calculate this~!
Posted 20 January 2009 - 04:50 AM
I'm very impressed.. Great job BigAnt!! 0 was the correct answer.
I doubt this is what you expected as answer but if you take the least significant digit of the first term and move it onto the equality character you get a not equal to sign.
10 - 102 != 1
I just figured the correct answer as well when posting.. Just move the 2 to make it an exponent..
101 - 10^2 = 1
I doubt this is what you expected as answer but if you take the least significant digit of the first term and move it onto the equality character you get a not equal to sign.
10 - 102 != 1
I just figured the correct answer as well when posting.. Just move the 2 to make it an exponent..
101 - 10^2 = 1
This post has been edited by Gloin: 20 January 2009 - 04:51 AM
#110
BigAnt
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Re: Calculate this~!
Posted 20 January 2009 - 07:42 AM
Yes the second one was what I was looking for 
The Puzzle: Two friends have a nice meal together, and the bill is $25
The friends pay $15 each, which the Waiter gives to the Cashier
The Cashier hands back $5 to the Waiter
The Waiter keeps $3 as a tip and hands back $1 each
So, the friends paid $14 each for the meal, for a total of $28. The Waiter has $3, and that makes $31. Where did the other dollar come from?
The Puzzle: Two friends have a nice meal together, and the bill is $25
The friends pay $15 each, which the Waiter gives to the Cashier
The Cashier hands back $5 to the Waiter
The Waiter keeps $3 as a tip and hands back $1 each
So, the friends paid $14 each for the meal, for a total of $28. The Waiter has $3, and that makes $31. Where did the other dollar come from?
This post has been edited by BigAnt: 20 January 2009 - 03:16 PM
#111
BigAnt
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Re: Calculate this~!
Posted 23 January 2009 - 09:31 AM
Actually someone already asked this, just with different numbers...
SO lets try this:
If one and a half hens lay one and a half eggs in one and a half days, how many eggs does one hen lay in one day?
SO lets try this:
If one and a half hens lay one and a half eggs in one and a half days, how many eggs does one hen lay in one day?
#113
BigAnt
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Re: Calculate this~!
Posted 23 January 2009 - 09:47 AM
Good guess!
Hens × Days × (DR) = Eggs
1 ½ × 1 ½ × (DR) = 1 ½
DR= 1 ½ / (1 ½ × 1 ½)
DR= 1/(1 ½) = 2/3
So 1 hen in 1 day will lay two-thirds of an egg
Now its your turn to post the problem
Hens × Days × (DR) = Eggs
1 ½ × 1 ½ × (DR) = 1 ½
DR= 1 ½ / (1 ½ × 1 ½)
DR= 1/(1 ½) = 2/3
So 1 hen in 1 day will lay two-thirds of an egg
Now its your turn to post the problem
#114
Auzzie
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Re: Calculate this~!
Posted 23 January 2009 - 08:04 PM
A box contains some buttons. 1/4 of them are black, 1/8 of them are red,
and the rest are white. There are 204 more white buttons than red buttons.
How many buttons are there altogether?
and the rest are white. There are 204 more white buttons than red buttons.
How many buttons are there altogether?
#119
BigAnt
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Re: Calculate this~!
Posted 25 January 2009 - 10:14 AM
Pythagorean Parallelepiped:
You may be familiar with Pythagorean triangles--triangle solutions of the equation x^2+y^2=z^2--such as 3,4,5: 5, 12, 13: etc. The problem now is to find a 3d example--a rectangular parallelepiped whose edges and diagonal can be expressed as integers--i.e., an integral solution of w^2+x^2+y^2=z^2. This problem should be solved mentally.
You may be familiar with Pythagorean triangles--triangle solutions of the equation x^2+y^2=z^2--such as 3,4,5: 5, 12, 13: etc. The problem now is to find a 3d example--a rectangular parallelepiped whose edges and diagonal can be expressed as integers--i.e., an integral solution of w^2+x^2+y^2=z^2. This problem should be solved mentally.
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