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?
[Ref: ZPYU] Mamma's Age. Amusements In Mathematics by Henry Ernest Dudeney (1917).
Hint: The answer involves years and months.
Answer: 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.
The answer above is taken from the original book, here is another version of the answer:
If we call Tommy T, Mamma M and Papa P we can see that:
"our three ages add up to exactly seventy years" leads to
T + M + P = 70 (1)
"Just six times as old as you" leads to
P = 6 x T (2)
In an unknown number of years (Y) "Shall I ever be half as old as you" leads to:
P + Y = 2 x (T + Y) (3)
and "our three ages will add up to exactly twice as much as to-day" leads to:
(T + Y) + (M + Y) + (P + Y) = 140
which can be written as
T + M + P + 3Y = 140 (4)
We can see from (4) and (1) that
3Y = 70
so
Y = 70 ÷ 3 (5)
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
T = 70÷12 (6)
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.
QED.
Puzzle 197
Below are ten words, from each word, remove a single letter and rearrange the remaining letters to find ten new words which are related to each other.
ENERGY
DOORMAN
CLEAREST
WEIGHT
OUTLIVE
EMBARK
CALMER
SOLEMN
VOIDING
ARCHERY
ENERGY - Y = GREEN
DOORMAN - D = MAROON
CLEAREST - E = SCARLET
WEIGHT - G = WHITE
OUTLIVE - U = VIOLET
EMBARK - K = AMBER
CALMER - L = CREAM
SOLEMN - S = LEMON
VOIDING - V = INDIGO
ARCHERY - A = CHERRY
Puzzle 198
Fred can eat 27 chocolates in a hour, Alice can eat 2 chocolates in 10 minutes, and Kelly can eat 7 chocolates in 20 minutes. How long will it take them to share and eat a large box of 120 chocolates whilst watching a movie?
Hint: In total how many chocolates are eaten each hour.
Answer: 2 hours.
In one hour, Fred eats 27 chocolates, Alice eats 12, and Kelly eats 21. A total of 60 chocolates. Therefore 120 chocolates would take 120 ÷ 60 = 2 hours. QED.
Puzzle 199
Each empty white square in the grid contains one of the numbers 1, 2, 3,..., 8. Each of the horizontal and vertical equations must be true and each number must be used exactly once.
Using the BrainTracker grid below, how many words can you find? Each word must contain the central H and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. There is at least one nine letter word. Excellent: 39 words. Good: 25 words. Average: 18 words.
Puzzle 196
