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In the tax year 2023/24 Tamsin had the following sources of income:

Employment income£41,000
Property income£45,000
Bank interest received£2,500
 Dividends received £20,000

She also paid a donation of £800 to a charity under the gift aid scheme.

What is the amount of personal allowance that Tamsin will be entitled to for the tax year 2023/24?

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We consider a variation on Euler Problem 215.

Walls are still built out of 2x1 or 3x1 bricks, but this time is it OK to have "running cracks" of length at most 2, as in the following 9x3 wall:

Example of acceptable 9x3 walls were the longest running cracks have length 2. 

However, longer running cracks are disallowed.  The following 9x3 wall is not acceptable because it has one running crack of length 3.

Example of 9x3 wall that should be rejected because it contains a running crack of length 3.

There are possible 9x3 walls in which the maximal length of running cracks is 2 or 1.

There are possible 10x4 walls in which the maximal length of running cracks is 2 or 1.

There are possible 11x5 walls in which the maximal length of running cracks is 2 or 1.

Compute the value of .

Hint: consider a graph whose vertices represent pairs of layers, such that an edge represents in acceptable superposition of the three layers , , and .

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Укажи, які характеристики має зростаючий тип статево-вікової піраміди

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Який тип вентиляції підтримує нормальне повітряне середовище в усьому об’ємі робочої зони приміщення:

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Quel est l'intervalle de solidification de l'acier à 1,3% de carbone?

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