Factoring out 2^2016 from both the numerator and the denominator:
results in 5/3.
Q: Two coins are flipped and you cannot see the outcome but are told that at least one is a head. What is the probability that the other coin also landed on heads?
This is a classic probability question. Once you know that one coin is a head, there are 3 possible outcomes for the two coins with at least one head.
Since you know that one is a heads, and there are 3 possible outcomes, the probability is 1/3.
Q: Write down all the integers from 1 through 60 to form the number
Now delete 100 digits from this number.
Without rearranging the digits, what is the largest number possible?
A: Writing down all integers from 1 through 60 gives you a number 111 digits long:
9 numbers at 1 digit apiece: 9 digits
51 numbers at 2 digits apiece: 102 digits
Total: 111 digits.
So deleting 100 digits leaves us with 11 digits. It’s be best to have as many 9’s as we can as far to the left as we can. But there’s only 6 of those, and one of them is already in the hundreds place before we do any deleting.
If we’re not allowed to rearrange the digits, the largest number is:
99 999 785 960.
Write the numbers from 1 to 8 into the squares, so that the squares with consecutive numbers do not touch
(neither edges nor corners).
Here is one version of a correct answer:
There are variations on this answer
such as the whole grid can be upside down (64 on top and 53 on bottom)
or it can be reversed left to right.
Q: Find the three digit number that when you multiply it by two, it is one more than the reverse of the original number.
For example, 102 doubled is 204 which is 3 more than the reverse (201).