Below are thirteen words, each of which has had two letters removed. The remaining letters are in the correct order. Between them, the thirteen words have had the letters A-Z removed, each once only. Can you find the original words?

BAG
DED
DIA
UOA
IDE
OEL
UMS
PYY
GOU
NAL
CRA
UMB
DTY

Hint: These are the first letters of the words: B, D, D, Q, I, V, B, P, G, F, C, J, D.

Answer:

BAG >> BADGE
DED >> DAZED
DIA >> DIARY
UOA >> QUOTA
IDE >> INDEX
OEL >> VOWEL
UMS >> BUMPS
PYY >> PYGMY
GOU >> GHOUL
NAL >> FINAL
CRA >> CRACK
UMB >> JUMBO
DTY >> DUSTY

Puzzle 2

Three men are buried in the sand all facing forwards with their heads above ground.

Each man has a hat placed on his head selected from a bag containing 3 red hats, and 2 black hats, and the men knew the possible hat choices.

The men cannot turn around to see the men behind them.

The man at the back is asked what hat he is wearing. He replies 'I do not know'. The middle man is asked what hat he is wearing. He also replies 'I do not know'. The man at the front is then asked what hat he is wearing. He replies 'I am wearing a red hat'.

How did he know?

[Ref: ZSAU]

Hint: Think about the man at the back first.

Answer:
Since the man at the back could not determine his own hat, this means that the front two men could not have been wearing black hats and that, therefore, there must be at least one red hat on the two front men.

Therefore the middle man must not be able to see a black hat otherwise he would know he had a red one on.

Therefore the front man must be wearing a red hat - which finally he deduces. Interestingly, the other two can never determine their own hats.

Puzzle 3

By changing the third letter of each of the words below, can you make another valid word.

You have to change each word such that the third letters will reveal a ten letter word when read downwards.

Therefore, what now reads KRZSAPROKD will be a real word.

At the recent BrainBashers Festival, the 100 metres heats were closely monitored.

Each contestant had to run in two races so that the average place could be determined.

Only one runner finished in the same place in both races.

Alan was never last. Charlie always beat Darren. Brian had at least one first place. Alan finished third in at least one of the races. Both Darren and Charlie had a second place.

To explain - since Charlie always beat Darren and Darren had a second place, one race must have been Charlie first and Darren second. Brian therefore won the other race with Charlie second. Since only one runner finished in the same place in both races, this must have been Alan in third. QED.

Puzzle 5

Practical Peter was asked to cut a 99 foot rope into three smaller, equal length ropes.

However, as usual, Pete couldn't find his measuring tape so he guessed!

When he finally did find his tape (it was under his hat), he discovered that:

A) the second piece of rope was twice as long as the first piece, minus 35 feet (i.e. 2 x first, - 35).
B) the third piece of rope was half the length of the first, plus 15 feet (i.e. 0.5 x first, + 15)