Medium Puzzles 

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.

Workings

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

Answer
Your friend.

Reasoning
You were dealt the Green Ace.

   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Blue King
   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 any Queen, so your friend can only have one of these cards:
   Green Jack
   Red Ace
   Blue Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Blue King
   Orange King
   Green King

By (2), their card is not more likely to beat yours (4 v 4), so their card is not Blue, leaving:
   Green Jack
   Red Ace
   Orange Ace
   Green Ace (your card)
   Red King
   Orange King
   Green King

By (3), your card is not more likely to beat theirs (3 v 3), so your friend's card is not a King, leaving:
   Green Jack
   Red Ace
   Orange Ace
   Green Ace (your card)

All of which beat your Green Ace.

Workings

Hint
Look closely at the beginnings and the ends of the words.

Answer
Ice.

Each word begins with the last two letters of the previous word.

Workings

Hint
The first word starts with H.

Answer
Hard and soft.