I N
2 4
H _ _ R S
T H _
W _ T C H
G _ _ N _ D
1 / 2 - 1 / 3 =
1 / 6
M _ N _ T _ .
I T
W _ _ L D
S _ _ M
_ T
W _ _ L D
B _
5
M _ N _ T _ S
F _ S T
_ N
5
X
6 =
3 0
D _ Y S ;
T H _ T
_ S , T H _
M _ R N _ N G
_ F
M _ Y
3 1 .
B _ T
_ L R _ _ D Y
_ N
T H _
M _ R N _ N G
_ F
M _ Y
2 8
T H _
W _ S
2 7 / 6 =
4
1 / 2
M _ N _ T _ S
F _ S T .
A T
T H _
C L _ S _
_ F
T H _
D _ Y
T H _
W _ T C H
G _ _ N _ D
1 / 2
M _ N _ T _
M _ R _ ,
S _
_ T
W _ S
5
M _ N _ T _ S
F _ S T
_ N
M _ Y
2 8 Clue
IN 24 HOURS THE WATCH GAINED 1/2-1/3= 1/6 MINUTE. IT WOULD SEEM IT WOULD BE 5 MINUTES FAST IN 5 X 6= 30 DAYS; THAT IS,THE MORNING OF MAY 31. BUT ALREADY ON THE MORNING OF MAY 28 THE WAS 27/6= 4 1/2 MINUTES FAST. AT THE CLOSE OF THE DAY THE WATCH GAINED 1/2 MINUTE MORE, SO IT WAS 5 MINUTES FAST ON MAY 28 THE STATION CLOCK IS 3 MINUTES FAST. THE MORNING JOURNEY TOOK 65 MINUTES, AND THE EVENING JOURNEY THEREFORE TOOK 52 MINUTES, AND THE TRAIN ARRIVED 57 MINUTES AFTER IT SHOULD HAVE LEFT, THAT IS, 3 MINUTES EARLY AS THE PROBLEM SAYS THE APPRENTICE MIXED UP THE HANDS SO THAT THE MINUTE HAND WAS SHORT AND THE HOUR HAND WAS LONG. THE FIRST TIME THE APPRENTICE RETURNED TO THE CLIENT WAS ABOUT 2 HOURS AND 10 MINUTES AFTER HE HAD SET THE CLOCK AT SIX.THE LONG HAD MOVED OLNY FROM TWELVE TO A LITTLE PAST TWO. THE LITTLE MADE TWO WHOLE CIRCLES AND AN ADDITIONAL 10 MINUTES. THUS THE CLOCK SHOWED THE CORRECT TIME. THE NEXT DAY AROUND 7:O5 A.M.HE CAME A SECOND TIME,13 HOURS AND 15 MINUTES AFTER HE HAD SET THE CLOCK FOR SIX. THE LONG HAD, ACTING AS THE HOUR HAND,COVERED 13 HOURS TO REACH 1. THE SHORT HAND MADE 13 FULL CIRCLES AND 5 MINUTES, REACHING 7, SO THE CLOCK SHOWED THE CORRECT TIME AGAIN LET: CAMPER 1 = C1 (1) CAMPER 2 = C2 (2) CAMPER 3 = C3 (5) CAMPER 4 = C4 (10) THIS IS HOW THEY CROSS THE BRIDGE: C1,C2 → (2) ← C2 (2) C3,C4 → (10) ← C1 (1) C1,C2 → (2) THE TIME IN BRACKETS () INDICATE THE TIME TAKEN TO CROSS THE BRIDGE. IF YOU SUM THEM UP, IT WILL ADD UP TO 17 MINUTES