You have a hand of cards that depict each of the letters of the alphabet. You fan the cards and see they are in the following order:

F, W, X, Y, Z, K, L, A, T, U, J, N, O, S, D, E, P, V, C, B, G, H, I, Q, R, M

Your job is to [...]

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Logic
Consider this series:

4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, …, …, …

What would the 50th, 63rd and 100th observations be?

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Series
For your next experiment, you have managed to round up an infinite number (give or take) of willing test subjects.

You also have a big slide with 100 holes in it.

As each of your test subjects go down the slide, they have a 50/50 chance of either going down the holes, or continuing down the [...]

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Maths Probability
I show you a shuffled deck of standard playing cards, one card at a time, no Jokers in the pack.

At any point before I run out of cards, you must say “RED!”.

If the next card I show is red (i.e. diamonds or hearts), you win.

As “dealer” I don’t have any control [...]

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Probability
An investor puts $10,000 into a weekly trading scheme.

In each week it is equally likely that he’ll make an 80% gain or a 60% loss (there are no other possibilities). One year later (52 weeks), roughly how much money does the investor expect to have? The answer is one of the following:

a) $1.95, b) $14,000, c) $140,000, [...]

Prove that for any natural number that ends in 1, 3, 7 or 9, that it has an infinite number of multiples which consists only of a string of 1’s.

e.g. 13*8547 = 111111

NB It is trivial to show that numbers ending in 0, 2, 4, 5, 6 or 8 cannot possses that property.

Four glasses are placed upside down in the four corners of a square

rotating table.

You wish to turn them all up. You may do so by grasping any two glasses and, optionally, turning either over.

There are two catches:

1. you are blindfolded

2. the table is spun after each time you move the glasses

Assuming that a bell [...]

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Logic
You have made a deal with the devil… You will win the lottery if you can decide the optimal position in the queue to buy the £163m Euromillions winning lottery ticket.

There are some conditions. Ain’t that always the way when making this sort of deal!

You will win, if your position in the queue is [...]

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Probability
The following sequence has a name…..but I don’t know what that is…. What’s the next number in the meantime….

2

12

360

75600

174636000

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Maths
What unknown value can you add to 1 in order to get one less?

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Tom