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Posts under Tom

A Roll of The Dice

Posted by Karl Sharman under Tom (6 Responds)

Suppose n fair 6-sided dice are rolled simultaneously. What is the expected value of the score on the highest valued die?

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Lowest Value of n is 404?

Posted by Karl Sharman under Tom (11 Responds)

Where the numbers 2n and 5n (where n is a positive integer) start with the same digit, what is the lowest possible value of n? The numbers are written in decimal notation, with no leading zeroes. I am going to get flak for this…. but, I have broad shoulders!

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If we are doing dice – try some different dice!

Posted by Karl Sharman under Tom (9 Responds)

With a standard pair of six sided dice, there is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:
a. The set of dots on each die is not the standard {1,2,3,4,5,6}.
b. Each face has [...]

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500 Triangles

Posted by Karl Sharman under Tom (5 Responds)

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 [...]

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Time Trial on Trust

Posted by Karl Sharman under Tom (9 Responds)

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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Let’s build another road

Posted by Zorglub under Tom (6 Responds)

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 [...]

f(2014)

Posted by Zorglub under Tom (36 Responds)

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 ?

Look at that S Car Go

Posted by Karl Sharman under Tom (16 Responds)

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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Who needs the Intel i7 chip?

Posted by Karl Sharman under Tom (3 Responds)

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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2 for all, and all for 2

Posted by Karl Sharman under Tom (6 Responds)

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.

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