John Heysham Gibbon was most renowned surgeon of 1940-1970. More than 90% of his surgeries he performed are highly successful and still almost all of his patients die.
The surgery was performed way back, by now approx 90% of them have died by old age.
A women walks into a bank to cash out her check.
By mistake the bank teller gives her dollar amount in change, and her cent amount in dollars.
On the way home she spends 5 cents, and then suddenly she notices that she has twice the amount of her check.
How much was her check amount?
The check was for dollars 31.63.
The bank teller gave her dollars 63.31
She spent .05, and then she had dollars 63.26, which is twice the check.
Let x be the dolars of the check, and y be the cent.
The check was for 100x + y cent
He was given 100y + x cent
Also
100y + x - 5 = 2(100x + y)
Expanding this out and rearranging, we find:
98y = 199x + 5
Which doesn't look like enough information to solve the problem except that x and y must be whole numbers, so:
199x ≡ -5 (mod 98)
98*2*x + 3x ≡ -5 (mod 98)
3x ≡ -5 ≡ 93 (mod 98)
This quickly leads to x = 31 and then y = 63
Alternative solution by substitution:
98y = 199x + 5
y = (199x + 5)/98 = 2x + (3x + 5)/98
Since x and y are whole numbers, so must be (3x + 5)/98.
Call it z = (3x+5)/98
so 98z = 3x + 5, or 3x = 98z - 5 or x = (98z - 5)/3
or x = 32z-1 + (2z-2)/3.
Since everything is a whole number, so must be (2z-2)/3.
Call it w = (2z-2)/3, so 3w = 2z-2 so z = (3w+2)/2 or
z = w + 1 + w/2. So w/2 must be whole, or w must be even.
So try w = 2. Then z = 4. Then x = 129. Then y = 262.
if you decrease y by 199 and x by 98, the answer is the same:
y = 63 and x = 31.
The Pope, Beyonce, POTUS, and Bill Gates are on the same plane.
There are only 3 parachutes left for the 4 of them.
POTUS says: "As the President, I think I should have the right to have a parachute, because I rule millions of people in the greatest nation of all."
Beyonce says: "As one of the greatest singers of all-time, I think I should deserve to be safe. I bring tears and laughter to millions of people, and I'm an important contributor to pop music."
Bill Gates says: "As one of the richest successful company owners, I think I should live because I'm on top of the economics cycle, creating jobs and incomes for millions of people. I am a wealthy and intelligent man."
Finally, the Pope says: "I'm an old, religious man. I lived a life that's full, I helped millions of people find their way through God, I'm ready to let go of a parachute and to face my fate."
Which one of them will abandon the parachute and die?
Did I ever mention that the plane was crashing? No one's gonna die.
Allan, Bertrand, and Cecil were caught stealing so the king sent them to the dungeon.
But the king decided to give them a chance.
He mad them stand in a line and put hats on their heads.
He told them that if they answer a riddle, they could go free.
Here is the riddle: "Each of you has a hat on your head. You do not know the color of the hat on your own head. If one of you can guess the color of the hat on your head, I will let you free. But before you answer you must keep standing in this line. You cannot turn around. Here are my only hints: there are only black and white hats. At least one hat is black. At least one hat is white."
Allan couldn't see any hats.
Bertrand could see Allan's hat but not his own.
Cecil could see Bertrand's hat and Allan's hat, but not his own.
After a minute nobody had solved the riddle. But then a short while later, one of them solved the riddle. Who was is and how did he know?
Bertrand knew the answer because Cecil didn't say anything after one minute. If Bertrand and Allan's hats were both the same color, then Cecil would know what color his hat was. But Cecil didn't know. So Bertrand knew that Allan's hat was a different color than his. Since Allan's hat was black, Betrand knew his hat was white.
