Coffee Time Challenges
続き。
Coffee Time Challenges
7) Legs
Challenge: In a room there are a mixture of people and dogs. There are 72 heads, and 200 legs. How many dogs are in the room? (No tricks, no chromosomal abnormalities, no disabilities …)
これ、要するに鶴亀算なんですがヒントを見ちゃうとですね
This is simple algebra. If you need to write code to solve this, please stop reading.
だそうです。
Coffee Time Challenges
8) One, Two, Three
Challenge: Using just one 1, one 2, and one 3 (no concatenation of digits) and any combination mathematical
symbols you wish (addition, subtraction, multiplication, division, parenthesis, exponents, factorial,
square root …). Write an equation to gives the total 19.
9) One, Seven
Challenge: As above, how about making a total of 71 using just one 1 and one 7 (again, no concatenation
of digits, or this would be trivial!)
この二つはプログラム組むのは面倒?
前者は sqrt((3!)!/2 + 1)
後者は sqrt(7! + 1)
10) Buckets
Challenge: Put the numbers 1-13 into three buckets with the constraint that the difference between any two
pairs of numbers in any bucket is not a number also in that bucket. (e.g. If you place 5,7 in a bucket,
then you cannot place 2 in that same bucket).
11) Product and Sum
Challenge: I’ve written down all the integers from 1 to 65,502 inclusive. I select two of them, cross them
out, and multiply them together to get a product. When I sum up the remaining 65,500 numbers, I get the same
result. What two numbers did I pick?
12) Adjacent Squares
Challenge: Arrange the integers 1-17 (inclusive) so that each adjacent pair of numbers is a perfect square.
e.g. 14, 2, 7 … (The first and last do not have to wrap around)
13) How many
Challenge: ABCDEFGHIJ is a ten-digit-number. All of the digits are distinct. If 11111 divides it evenly,
how many possibilities are there for ABCDEFGHIJ?
14) Reciprocals
Challenge: Find six distinct integers: A, B, C, D, E, F the reciprocals of which add up to exactly one.
e.g. 1/A + 1/B + … 1/F = 1
この辺は単純な力業では組み合わせの威力の前に撃破されてしまうので
さてどうしましょ。