S _ B R _ N _
H _ D
$ 5 0
_ N D
S _ M _ N T H _
H _ D
$ 3 0 .
T H _ S
C _ N
B _
S _ L V _ D
B Y
S _ T T _ N G
_ P
T W _
S _ M _ L T _ N _ _ _ S
_ Q _ _ T _ _ N S ,
B _ T
_ T ' S
_ _ S _ _ R
J _ S T
T _
W _ R K
B _ C K W _ R D S .
A T
_ _ C H
S T _ P ,
T H _
P _ R S _ N
W H _
_ S
R _ C _ _ V _ N G
T H _
M _ N _ Y
G _ T S
T H _
_ M _ _ N T
T H _ T
T H _ Y
W _ R _
_ L R _ _ D Y
H _ L D _ N G .
I N
_ T H _ R
W _ R D S ,
T H _ Y
D _ _ B L _
T H _ _ R
M _ N _ Y .
T H _ R _ F _ R _ ,
J _ S T
B _ F _ R _
T H _
L _ S T
_ X C H _ N G _ ,
S _ M _ N T H _
M _ S T
H _ V _
H _ D
$ 4 0
_ N D
W _ S
G _ V _ N
_ N _ T H _ R
$ 4 0
T _
G _ T
T _
H _ R
T _ T _ L
_ F
$ 8 0 .
J _ S T
B _ F _ R _
T H _
S _ C _ N D
_ X C H _ N G _ ,
S _ B R _ N _
M _ S T
H _ V _
H _ D
H _ L F
_ F
H _ R
$ 4 0 .
T H _ R _ F _ R _ ,
S _ B R _ N _
H _ D
$ 2 0
_ N D
S _ M _ N T H _
H _ D
$ 6 0 .
A F T _ R
T H _
F _ R S T
_ X C H _ N G _
S _ M _ N T H _
D _ _ B L _ D
H _ R
M _ N _ Y ,
S _
S H _
M _ S T
H _ V _
H _ D
$ 3 0
B _ F _ R _
T H _
_ X C H _ N G _ ,
L _ _ V _ N G
S _ B R _ N _
W _ T H
$ 5 0
_ T
T H _
S T _ R T Clue
THE PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CONCEAL WHAT IS REALLY GOING ON. LET'S LOCATE ALL THAT MONEY. THERE ARE TWO WAYS TO THINK ABOUT HOW MUCH MONEY IS OUT THERE TO BE FOUND.THE WAY THAT THIS QUESTION IS TRICKY IS THAT IT COMBINES THAT TWO WAYS. THE FIRST WAY IS THIS. HOW MUCH MONEY DID MOM AND DAD PAY ORIGINALLY? THE SECOND WAY IS THIS. HOW MUCH MONEY DID THEY END UP PAYING? SO IF IT IS THE FIRST WAY, THEN CLEARLY THE TOTAL WE NEED TO ACCOUNT FOR IS THE $100. SO LET'S SEE WHAT HAPPENS TO THAT $100. THE SHIRT COSTS $97, THE BOY KEEPS $1 AND MOM AND DAD GET $1 BACK. THAT ADDS UP FINE. NOW LET'S LOOK AT THE SECOND WAY. HOW MUCH MONEY DID THEY END UP PAYING? WELL $98 DOLLARS, AND $97 OF IT WENT FOR THE SHIRT AND $1 TO THE BOY. NOW, THAT ADDS UP TOO. THE PROBLEM WITH THE QUESTION IS THAT THE THE $1 THAT THE BOY KEEPS IS CONTAINED IN THE $98 THAT THEY END UP PAYING SO WE SHOULDN'T EXPECT THEM TO ADD TO ANYTHING MEANINGFUL 25 EGGS WERE BROKEN. THERE IS ONLY ONE WAY OF FINDING A SOLUTION TO THIS PROBLEM: NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 4: 5, 9, 13, 17, 21, 25, 29, 33, 37 NUMBERS WHICH LEAVE NO REMAINDER WHEN DIVIDED BY 5: 5, 10, 15, 20, 25, 30, 35 THE ONLY NUMBER FULFILLING THE FOUR CONDITIONS IS 25 THE PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CONCEAL WHAT IS REALLY GOING ON. LET'S LOCATE ALL THAT MONEY. THERE ARE TWO WAYS TO THINK ABOUT HOW MUCH MONEY IS OUT THERE TO BE FOUND.THE WAY THAT THIS QUESTION IS TRICKY IS THAT IT COMBINES THAT TWO WAYS. THE FIRST WAY IS THIS. HOW MUCH MONEY DID THE GUYS PAY ORIGINALLY? THE SECOND WAY IS THIS. HOW MUCH MONEY DID THEY END UP PAYING? SO IF IT IS THE FIRST WAY, THEN CLEARLY THE TOTAL WE NEED TO ACCOUNT FOR IS THE $30. SO LET'S SEE WHAT HAPPENS TO THAT $30. THE MANAGER KEEPS $25, THE BELLBOY GETS $2 AND THE GUYS GET $3 BACK. THAT ADDS UP FINE. NOW LET'S LOOK AT THE SECOND WAY. HOW MUCH MONEY DID THEY END UP PAYING? WELL $27 DOLLARS, AND $25 OF IT WENT TO THE OWNER AND $2 TO THE BELLBOY. NOW, THAT ADDS UP TOO. THE PROBLEM WITH THE QUESTION IS THAT THE THE $2 THAT THE BELLBOY GETS ARE CONTAINED IN THE $27 THAT THEY END UP PAYING SO WE SHOULDN'T EXPECT THEM TO ADD TO ANYTHING MEANINGFUL SABRINA HAD $50 AND SAMANTHA HAD $30. THIS CAN BE SOLVED BY SETTING UP TWO SIMULTANEOUS EQUATIONS, BUT IT'S EASIER JUST TO WORK BACKWARDS. AT EACH STEP, THE PERSON WHO IS RECEIVING THE MONEY GETS THE AMOUNT THAT THEY WERE ALREADY HOLDING. IN OTHER WORDS, THEY DOUBLE THEIR MONEY. THEREFORE, JUST BEFORE THE LAST EXCHANGE, SAMANTHA MUST HAVE HAD $40 AND WAS GIVEN ANOTHER $40 TO GET TO HER TOTAL OF $80. JUST BEFORE THE SECOND EXCHANGE, SABRINA MUST HAVE HAD HALF OF HER $40. THEREFORE, SABRINA HAD $20 AND SAMANTHA HAD $60. AFTER THE FIRST EXCHANGE SAMANTHA DOUBLED HER MONEY, SO SHE MUST HAVE HAD $30 BEFORE THE EXCHANGE, LEAVING SABRINA WITH $50 AT THE START