Medium Puzzles 

Workings

Hint
List all of the cards, and then eliminate some using (1).

Answer
You.

Reasoning
You were dealt the Blue King.

The possible cards, in order, are:
   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace
   Red King
   Blue King (your card)
   Orange King
   Green King
   Red Queen
   Blue Queen
   Orange Queen
   Green Queen
   Red Jack
   Blue Jack
   Orange Jack

By (1), your friend's card is higher than the Green King, so your friend can only have one of the following cards:

   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace
   Red King
   Blue King (your card)
   Orange King

By (2), their card is more likely to be a Jack (1) than a Queen (0), so their card is a King. Leaving:

   Red King
   Blue King (your card)
   Orange King

By (3), only 1 could beat your card, so it is not more likely to beat yours, therefore their card is not Red. Leaving:

   Blue King (your card)
   Orange King

So your friend must have the Orange King, which your card beats.

Workings

Hint
The first 6 words begin with the letters D, A, Q, S, W, S.

Answers
---amt = dreamt ---nue = avenue ---rtz = quartz ---oze = snooze ---mth = warmth ---iek = shriek ---gry = hungry ---thm = rhythm ---koo = cuckoo ---spy = crispy ---sip = gossip ---lem = emblem ---uid = liquid ---tyr = martyr ---meg = nutmeg

Workings

Hint
The first word begins with the letter A.

Answers
-s-e-d = ascend -p-a-g = sprang -r-f-r = prefer -y-r-d = hybrid -r-f-e = trifle -a-b-n = carbon -a-e-a = camera -o-d-g = hotdog -s-f-l = useful -i-s-e = tissue

Workings

Hint
The answer isn't a whole number of years, and algebra might be required.

Answer
29 years 2 months.

Reasoning #1
This answer is taken directly from the original book.

The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.

Reasoning #2
Here's my answer, with a little algebra.

If we call Tommy T, Mamma M and Papa P we can see that:

"our three ages add up to exactly seventy years" gives us:

(1)   T + M + P = 70

"Just six times as old as you" gives us:

(2)   P = 6 x T

In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:

(3)   P + Y = 2 x (T + Y)

and "our three ages will add up to exactly twice as much as today" gives us:

   (T + Y) + (M + Y) + (P + Y) = 140

which can be written as

(4)   T + M + P + 3Y = 140

We can see from (4) and (1) that

     3Y = 70

so

(5)   Y = 70 ÷ 3

Using (2) and (5) in (3) we have

            P + Y = 2 x (T + Y)

   6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)

            4 x T = 70 ÷ 3

(6)             T = 70 ÷ 12

We can now use (6) in (2) to see that:

   P = 6 x T

   P = 6 x 70 ÷ 12

   P = 70 ÷ 2

And using the values for T and P in (1) we have:

              T + M + P = 70

   70 ÷ 12 + M + 70 ÷ 2 = 70

Multiply throughout by 12 to give:

   70 + 12 x M + 420 = 840

              12 x M = 840 – 420 – 70

              12 x M = 350

                   M = 350 ÷ 12

So:

   Tommy = 70 ÷ 12   = 5.83333  = 5 years 10 months.
   Papa  = 70 ÷ 2    = 35       = 35 years.
   Mamma = 350 ÷ 12  = 29.1666  = 29 years 2 months.