## Non-prime series

Show that no member of the infinite series:

10001, 100010001, 1000100010001, 10001000100010001, … is prime.

Warning: this one might be hard. e.g. the 18th term’s smallest prime factor is 722817036322379041

Posts under MathsChallenge

Posted by Chris under MathsChallenge (6 Responds)

Show that no member of the infinite series:

10001, 100010001, 1000100010001, 10001000100010001, … is prime.

Warning: this one might be hard. e.g. the 18th term’s smallest prime factor is 722817036322379041

Posted by Chris under MathsChallenge (11 Responds)

A set of positive integers is defined to be wicked if it contains no three consecutive integers. Count the sets with 0, 1 or 2 elements as wicked sets. Find the number of wicked subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it helps, define good sets as [...]

Posted by Chris under MathsChallenge (13 Responds)

A deck of cards is dealt to four players i.e. they get thirteen cards each.

What is the probability that exactly one of the players gets a complete suit?

Posted by Chris under MathsChallenge (7 Responds)

If p, q and r are prime, and p divides qr − 1, q divides rp − 1, and r divides pq − 1, find all possible values of pqr

Posted by Chris under MathsChallenge (22 Responds)

If you can take 1, 2 or 3 steps at a time, how many different ways are there to climb 6 steps?

Don’t try for a general closed formula, it can be done, but it’s horrible. There is a nice generating function though.

Posted by Chris under MathsChallenge (26 Responds)

You have three boxes and six marbles. If you randomly place the marbles in the boxes, what is the probability that you’ll place two marbles in each box?

Posted by Chris under MathsChallenge (2 Responds)

n points are selected on a circle. Every point is joined to the others by a line (a chord). What is the maximum number of intersections of the chords inside the circle and outside the circle?

Posted by Chris under MathsChallenge (5 Responds)

In a group of children and one adult there are b boys and g girls. If the average weight of the boys is g and the average weight of the girls is b, and the average weight of the whole group including the adult, whose weight is 42, is b + g. What is b [...]

There are three fair dice, each numbered 1 through 6; one Blue, one Red, and one Yellow.

You and your opponent will each pick one die and roll. Highest number wins*.

*Special cases:

If there is a tie, and the values are EVEN: Blue beats Red, Red beats Yellow, and Yellow beats Blue.

If there is a tie, and [...]

Posted by Chris under MathsChallenge (7 Responds)

Find any/all 6 digit numbers that are squares. The catch is, that the last 3 digits is 1 more than the first 3 digits. e.g. the number might look like 123124 (but that isn’t a square).

If there aren’t any such numbers, prove it.