Exercise of the Week #14

We’re back with some English after a little break!

Last Week’s Answers

This puzzle is known as a ‘cryptarithm’. Aside from being quite fun, they appear frequently in mathematical challenges, so it’s good to have a method for tackling them.

To solve cryptarithms, we must use logic and pattern recognition.

Note that F can only be 1, as even if both of the hundreds’ digits were 9, the maximum value for F would be 1.

Then, we know that the digits in the tens and ones’ positions must be the same.

We can use trial and error of values to work out the rest: given there are only a small number of possibilities, it shouldn’t take a prohibitively long time.

If we use these tips, we will find out that SUN + FUN = FANS represents 874 + 174 = 1048.

Exercise of the Week #8

Back to English today; a model answer with guidance will be posted underneath next week’s exercise.

Last Week’s Answers

1)      I imagine you’ve written a cube! There are some much more complicated alternatives (such as a triangular bipyramid) but we don’t need to know about those for now…

2)      A cylinder is comprised of a rectangle and two circles. You can remember this as a cylinder is shaped like a tin: there’s a circular lid and base and a rectangular label.

3)      A pentagonal prism is effectively a 3D pentagon. The definition of a prism is a shape which has the same cross-section at all points along one of its dimensions. In this case, that shape is a pentagon.

4)      A square-based pyramid has five vertices and eight edges. Multiply these to get 40. A trickier one to spot.

5)      A sphere, when cut, will always give a circle. This circle is largest when you cut directly through the centre.

6)      Which 2D shape has angles which add to 720? You may know that this is a hexagon. Each of the internal angles of a hexagon is 120, and there are 6. As it looks like a rectangle from above, we must be thinking of a hexagonal prism.

Exercise of the Week #2

Our exercise this week looks at persuasive writing. A model answer will be provided next week. Good luck!

Last Week’s Answers

1) She starts with £3000, but the King takes half, leaving her with £1500. However, he then gives her £500, which means she now has £2000. Then, the Chancellor takes one quarter, which is £500, leaving her with £1500.

2) Work backwards: if the Chancellor takes one quarter, Fred must have had £4000 after receiving money from the King. Now, take away the £500 he received. He’s got £3500. This is after the King has taken half - so we need to double it, giving us our final answer of £7000.

3) If I don’t have any money, the King takes half of 0, which is 0. But then, he gives us £500 regardless! But don’t get too excited: the Chancellor takes one quarter (£125) leaving us with £375. Nice!

4) If I’m left with £4125, this is after one quarter has been taken. So, £4125 is three-quarters of what we had before the Chancellor took his tithe. We need to know the full amount, four-quarters, so we can divide by 3 and multiply by 4 to give £5500. This is after the King gave us £500, so take that off: £5000. Finally, this is after the King halved our money, so double it: £10,000.