Answer
Here are the contents of the containers after each stage:
A = 9 litres, B = 4 litres
A B
9 0 fill A
5 4 fill B from A (leaving 5 litres in A)
5 0 empty B
1 4 fill B from A (leaving 1 litre in A)
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A (only 3 more litres fit in B)
6 0 empty B
This leaves 6 litres in container A.
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Puzzle 3
During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples.
During the night, Alex woke up and decided to hide some of the apples and hid a third, then promptly fell asleep again.
Billie woke up shortly after and also decided to hide a third of the remaining apples and then also dozed back to sleep.
Finally, Charlie woke up and seeing the others were asleep, took a third of what was left.
Of course, none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?
Hint
How many apples were left after Charlie had taken some?
Answer
162 apples.
Alex hid 54, leaving 108.
Billie then hid 36, leaving 72.
Charlie then hid 24, leaving 48 available to share in the morning.
Reasoning
To work these numbers out, we start at the end and work backwards.
At the end there were 16 apples each, therefore there were 48 apples in total.
Charlie removed one third, leaving 48, so there must have been 72 apples before.
Billie removed one third, leaving 72, so there must have been 108 apples before.
Alex removed one third, leaving 108, so there must have been 162 apples before.
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Puzzle 4
Below, 10 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 words are?
cer ent ead rat uti spr
ful oun pro ann ope ock
nce een oat est liv ion
nou sev ion ast hou akf
bre bea ens dim bed seb
Hints
The first letters of the words are: P, B, D, L, O, A, B, H, S, B.
Answers
pro + nou + nce = pronounce
bea + uti + ful = beautiful
dim + ens + ion = dimension
liv + est + ock = livestock
ope + rat + ion = operation
ann + oun + cer = announcer
bed + spr + ead = bedspread
hou + seb + oat = houseboat
sev + ent + een = seventeen
bre + akf + ast = breakfast
