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## Can You Bet Better?

Posted by Karl Sharman under Tom (4 Responds)

Would you take this bet?
Your friend he’s going to pick two different random numbers from a distribution not known to you. He will then write the two numbers of two small pieces of paper and put each one in each of his enclosed hands. You then pick a hand and he will reveal the [...]

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## Easy Maths Primer

Posted by Karl Sharman under Tom (3 Responds)

The prime 41, can be written as the sum of six consecutive primes:
41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.
The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and [...]

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## 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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## 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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