After the local BrainBashers Horse Show, some friends were telling everyone who had won.
Unfortunately, the friends were having trouble remembering, and in the course of the afternoon, they changed their minds a number of times.
In summary, they made the following statements:
Andy said: Taylor Tripton won with Evening Sunrise. Alex Ambleton won with Morning Sunset. Frankie Flanton won with Evening Sunrise. Billie said: Sam Spinton won with Midday Night. Frankie Flanton won with Evening Sunrise. Taylor Tripton won with Morning Sunset. Chris said: Alex Ambleton won with Midday Night. Sam Spinton won with Midday Night. Sam Spinton won with Morning Sunset. Dale said: Alex Ambleton won with Evening Sunrise. Frankie Flanton won with Morning Sunset. Sam Spinton won with Midday Night.
However, none of the statements were fully true.
In fact, just six of the statements were exactly half true (either the person won, or the horse did), the rest were false.
Can you determine who won, and which horse they were showing?
Reasoning
Before we begin the reasoning, let's look at the hint: 'Could Alex Ambleton have won?'. There are three horses in the puzzle, and Alex Ambleton is stated to have won with all three of them. We know that none of the statements were fully true, so Alex couldn't have won otherwise one of the statements would have been fully true.
However, we don't need the hint to solve the puzzle.
By grouping the clues together, we have:
1. Frankie Flanton won with Morning Sunset.
2. Frankie Flanton won with Evening Sunrise.
3. Frankie Flanton won with Evening Sunrise.
4. Sam Spinton won with Midday Night.
5. Sam Spinton won with Midday Night.
6. Sam Spinton won with Midday Night.
7. Sam Spinton won with Morning Sunset.
8. Taylor Tripton won with Morning Sunset.
9. Taylor Tripton won with Evening Sunrise.
10. Alex Ambleton won with Midday Night.
11. Alex Ambleton won with Morning Sunset.
12. Alex Ambleton won with Evening Sunrise.
We know that none of these statements were fully true, so, we know that (for example) it wasn't Frankie Flanton with Morning Sunset.
We can create a grid of all the possibilities and place an X where we know that it can't have been that combination:
M-N
M-S
E-S
Frankie
X
X
Sam
X
X
Taylor
X
X
Alex
X
X
X
We now have an X for all but 3 possibilities, and we know that exactly 6 of the clues must be half true.
So …
… if it was Frankie Flanton with Midday Night then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).
… if it was Sam Spinton with Evening Sunrise then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).
… if it was Taylor Tripton with Midday Night then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10), and this must be the correct answer.
??
Puzzle 2
Can you find a three-digit number such that when you reverse the numbers you get a larger number and the product of these two numbers is 224455?
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.
?
Puzzle 4
During the recent BrainBashers cipher convention, a Morse code contest took place.
The contest consisted of a Morse code transmission where the spaces between the letters and words were missing.
Can you find the ten animals?
Luckily, BrainBashers has provided you with a list of the Morse code characters:
