Puzzle 69
Below are 8 Academy Award winners.
The letters of their names have been mixed up and put into alphabetical order.
The brackets contain clues to their names, the first letter and the length of each part of their name. For example, EEIKNNOSTV [K5 S5] = KEVIN STONE.
DEEFIJOORST [J5 F6]
EEELMPRRSTY [M5 S6]
ABEIJLORRSTU [J5 R7]
AABEEHHIKNNPRRTU [K9 H7]
CEEEGGLNOOORY [G6 C7]
ACCHIJKLNNOOS [J4 N9]
BDEEINOORRRT [R6 D2 N4]
AACCEEHIILMN [M7 C5]
Puzzle Copyright © Kevin Stone
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Hint
One of the winners is called Jack.
Answer
DEEFIJOORST = JODIE FOSTER
EEELMPRRSTY = MERYL STREEP
ABEIJLORRSTU = JULIA ROBERTS
AABEEHHIKNNPRRTU = KATHARINE HEPBURN
CEEEGGLNOOORY = GEORGE CLOONEY
ACCHIJKLNNOOS = JACK NICHOLSON
BDEEINOORRRT = ROBERT DE NIRO
AACCEEHIILMN = MICHAEL CAINE
Puzzle 70
Can you find a five-digit number that …
… if you place a 9 at the beginning is four times larger than if you place a 9 at the end instead?
Puzzle Copyright © Kevin Stone
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Hint
What's a mathematical way to describe placing a 9 at the beginning?
Answer
23,076.
Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).
Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).
Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:
k + 900,000 = 4 x (10k + 9)
k + 900,000 = 40k + 36
900,000 – 36 = 40k – k
899,964 = 39k
899,964 ÷ 39 = k
Therefore, k = 23,076.
Double-Checking
923,076 = 4 x 230,769.
Puzzle 71
At midnight at the start of January 1st, Professor Stone set two old-fashioned clocks to the correct time.
One clock gains one minute every hour, and the other clock loses two minutes every hour.
When will the clocks next show the same time as each other?
When will the clocks both show the correct time?
Puzzle Copyright © Kevin Stone
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Hint
In order for the clocks to show the same time (e.g. 2 o'clock), what must the total time gained by one, and lost by the other, total?
Answers
Midnight, 10 days later, when they will both show 4 o'clock.
Midnight, 30 days later, when they will both show 12 o'clock.
Reasoning #1
In order for the clocks to show the same time, the total time gained by one, and lost by the other, must be 12 hours.
For example, if the first clock were to show 2 o'clock, it would have gained 2 hours. In order for the second clock to also show 2 o'clock, it would have had to have lost 10 hours. This is a total of 12 hours gained and lost.
We know that for every hour that passes, the first clock gains one minute, and the second clock loses 2 minutes, for a total time gained and lost of 1 + 2 = 3 minutes.
The total time gained and lost will equal 12 hours when 12 x 60 ÷ 3 = 240 hours have passed. 240 hours = 10 days.
The first clock will have gained 240 x 1 minutes = 240 minutes = 4 hours.
The second clock will have lost 240 x 2 minutes = 480 minutes = 8 hours.
So, they will both show 4 o'clock, 10 days later.
Reasoning #2
In the first answer, we can see that 10 days later, the clocks both show 4 o'clock.
If we move forward another 10 days, both clocks would show 8 o'clock.
If we move forward another 10 days, both clocks would show 12 o'clock.
This will now be the correct time.
So, they will both show 12 o'clock, 30 days later.
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