## The Staircase

It is possible to climb three steps in exactly four different ways.

Ie:-

step 1 step 2 and step 3

step 1 step 3

step 2 step 3

step 3

How many ways can you climb ten steps? And for further entertainment – twenty steps?

Archive for January, 2011

Posted by Karl Sharman under Tom (13 Responds)

It is possible to climb three steps in exactly four different ways.

Ie:-

step 1 step 2 and step 3

step 1 step 3

step 2 step 3

step 3

How many ways can you climb ten steps? And for further entertainment – twenty steps?

Posted by Chris under Logic (139 Responds)

From the old ToM site, but severely edited. It got 63 replies.

I have three children. If at least one of them is a girl, what is the probability that all three of them are girls?

—–

See post 130 for a link to a Monte Carlo simulator.

Posted by Karl Sharman under Tom (9 Responds)

For a set of 5 whole numbers, the mean is 4, the mode is 1 and the median is 5. What are the 5 numbers?

Tags: Maths
Posted by Karl Sharman under Tom (21 Responds)

Using the digits 1,2,3 & 4 and any of the basic rules of maths – add, subtract, divide, multiply and parentheses, what is the first natural, positive integer that cannot be obtained?

Tags: Maths
Posted by Karl Sharman under Tom (14 Responds)

There are 3 different pairs of positive integers that add up to make 6:-

1+5=6

2+4=6

3+3=6

So how many different pairs of positive integers are there to make up 1,000?

As that is too easy, part 2 of the question…. How many different triplets of positive integers add up to make 1,000, and of course, how many different quads [...]

Posted by Chris under MathsChallenge (13 Responds)

I found this on the old ToM site:

Let N be a positive integer. Find the smallest value of N (and the associated value of Y) such that 29*N = YNY (positional notation), where 1 ≤ Y ≤ 9.

e.g. I want something like: 345 * 29 = 23452

That example doesn’t work as the equation is false.

No [...]

Posted by Al Gelman under Tom (37 Responds)

This is a tough one.

What is the next number in this sequence:

1,4,9,16, …

Note: the answer is NOT 25

Posted by Chris under Logic (14 Responds)

You have 1025 coins in a bag. One of them is double headed. You pick one at random and flip it 10 times and get 10 heads. What is the probability that you had selected the double-headed coin?

Posted by Karl Sharman under Tom (14 Responds)

1. Karl has half the Jelly Babies that Chris has. Wiz has 3 times as many as Karl. Together they have 72. How many Jelly Babies does each one have?

2. I am 14 inches taller than Al Gelman. The difference between myself and Nordtorp is two inches less than between Nordtorp and [...]