The 100th digit to the right of the decimal point
Community Category: Math
Math problems submitted by Puzzle Prime’s community
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Plowing Snow
Snow has started falling some time before noon at a constant rate. At noon you start plowing from city A to city B, removing the snow at a constant volume per minute. If at 1PM you are 2 miles away from from city A, and at 2PM you are 3 miles away from city A, when did the snow start falling?
A Prime Puzzle
Change 3659 to 8101 by changing one digit at a time. Sounds easy. There is a catch! All numbers have to be four-digit primes. There is a unique shortest solution in 6 changes. If you like it I can publish more.
Outrun
Two friends – Usain and Tyson are racing each other over 100 meters dash. Usain wins by 10 meters. They decide to race again, but in order to even things up, Usain starts 11 meters behind the start line. Assuming both of them are running with constant speeds, the same as before, who will win?
Consecutive Numbers: Sums of Digits Divisible by 7
Find the two smallest consecutive integers so that the sum of the digits of each of them is divisible by 7.
Consecutive integer sequence
Find a consecutive integer sequence – n, n+1, n+2, …., n+k such that there does not exist a number in the sequence which is co-prime to all the other numbers in the sequence.
For example, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 is NOT such a sequence because 7 is co-prime to all the other numbers in the sequence.
Sequence Puzzle
Let a1,a2,a3,…. be the sequence of positive integers, such that each integer occurs exactly once. Prove that there exists 1<m<n , such that a1+an=2am