Hint
Find anagrams of the words in this order: PLEASE, TRANCE, LISTEN, WARNED, VEINED, BRUISE.
Answer
ANSWER.
Reasoning
The initial letters are RWASEN, which is an anagram of ANSWER. bruise becomes rubieswarned becomes wander (or warden)please becomes asleeplisten becomes silentveined becomes envied (or endive)trance becomes nectar
The word DEBATE can also be made, but this requires an obscure anagram.
At the local games evening, four friends were competing in the chess and croquet competitions.
Frankie beat Glen in chess, Dale came third, and the 16-year-old won. Frankie came second in croquet, the 15-year-old won, Dale beat the 18-year-old, and the 19-year-old came third. Emery is 3 years younger than Glen. The person who came last in chess came third in croquet, and only one person got the same position in both games.
Can you find the ages of the people and their positions in the two games?
Breaking the clues down, and numbering them: Frankie beat Glen in chess.Dale came third (chess).The 16-year-old won (chess).Frankie came second in croquet.The 15-year-old won (croquet).Dale beat the 18-year-old (croquet).The 19-year-old came third (croquet).Emery is 3 years younger than Glen.The person who came last in chess came third in croquet.Only one person got the same position in both games.
By (4), Frankie came 2nd in croquet. Name Age Chess Croquet
Dale
Emery
Frankie 2
Glen
By (2), Dale came 3rd in chess. Name Age Chess Croquet
Dale 3
Emery
Frankie 2
Glen
By (8), Emery is 15 or 16, and Glen is 18 or 19.
By (9), the person who came 4th in chess, came 3rd in croquet, and by (7), they are 19. This can't be Dale (3rd in chess), or Frankie (2nd in croquet), or Emery (aged 15 or 16), so it must be Glen. Name Age Chess Croquet
Dale 3
Emery
Frankie 2
Glen 19 4 3
By (6), Dale can't have been 4th in croquet, so must be 1st. Leaving Emery in 4th. Name Age Chess Croquet
Dale 3 1
Emery 4
Frankie 2
Glen 19 4 3
By (10), only one person got the same position in both games, this can't be Emery 4th in both (as Glen is already 4th in chess), so must be Frank, 2nd in both. Leaving Emery 1st in chess. Name Age Chess Croquet
Dale 3 1
Emery 1 4
Frankie 2 2
Glen 19 4 3
By (3) and (5) we know the ages of the winners in each competition, and Frankie is therefore 18. Name Age Chess Croquet
Dale 15 3 1
Emery 16 1 4
Frankie 18 2 2
Glen 19 4 3
Reasoning
My first is in bridge, but not in ridge = B
My second is in awake, and in mistake = A K E
My third is in danger, but not in ranger = D
My fourth is in strange, and in orange = R A N G E
My fifth is in spline, and in nine = I N E
My last is in river, and in diver = R I V E
??
Puzzle 208
Tommy: "How old are you, mamma?"
Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."
Tommy: "That's a lot, isn't it? And how old are you, papa?"
Papa: "Just six times as old as you, my son."
Tommy: "Shall I ever be half as old as you, papa?"
Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."
Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing--"
Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."
Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?
Mamma's Age, Amusements In Mathematics, Henry Ernest Dudeney.
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.
