A sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.

The first 7 terms would be: 1, 3, 6, 10, 15, 21, 28

Let us list the factors of the first seven triangle [...]

Tags:

Maths
I have a selection of 4 fairly easy puzzles. You can do these in your head. Time yourself, and, if you dare – publish your time along with the answers. Read the questions carefully, and your time starts……. NOW!

1. A large water tank has two inlet pipes (a large one and a small one) and one [...]

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Maths
Every day, a large number of people commute from city A to D by going through B and C. There are 4 roads

and the travel times are

A-B 40 minutes

C-D 40 minutes

The travel times on the two other roads depend on the proportion of traffic that uses them. Let p be the proportion of the [...]

An increasing sequence of integers is said to be alternating if it starts with an odd term, the second term is even, the third term is odd, the fourth is even, and so on. The empty sequence (with no term at all!) is considered to be alternating.

Let A(n) denote the number of alternating sequences which [...]

f is a function that maps a positive integer to a positive integer, and satisfy the properties f(n+1) > f(n) and f(f(n)) = 3n for every integer n.

a) what is f(2014) ?

b) Is f uniquely defined ? If so, what is its expression ?

Not many of you will be aware of my proud collection of racing snails. I have 8 of the speedy little critters. So fast are they, that I have an elaborate camera set up for those inevitable photo finishes.

Bonus point for identifying the title quote!

In how many ways, counting ties, can my 8 Racing [...]

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Maths
Here is a question that I recently uncovered. I didn’t find the answer with the question though. For big bonus points, and a gold star – When was the question written?

The Intel clock-doubled 486DX2-66 CPU chip operates by executing a certain fraction x of instructions totally on chip at a doubled rate (66 MHz), while [...]

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Maths
As an example, 64 is 2^6. Interestingly, take away the first number (6) and you are left with 4, which is 2^2 – So…find all the powers of 2 such that, after deleting the first digit, another power of 2 remains. Base 10, no leading zeroes etc.

Tags:

Maths
Two of my students, Dumber and Dumberer play a game based on the total roll of two standard dice. Dumber posits that a 12 will be rolled first. Dumberer says that two consecutive 7s will be rolled first.

They keep rolling until one of them wins. What is the probability that Dumber will win?

Tags:

Probabilities
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