Monday Maths Madness 25

Yeah... so I was too busy/tired to post the answers to last week's Maths Madness. Never fear! I will do it today. I will also put pictures in for your enjoyment :)

1. Take your house number and double it. Add 5. Multiply by 50. Then add your age, the number of days in the year, and subtract 615. The last two digits are your age, and the first two are your house number. Can you explain why?

If you turn this question into algebra, it is so much easier to understand. Say that your house number is x and your age is y. Then the question tells you to do this:

(2x + 5)*50 + y + 365 - 615. But this simplifies down to:

100x + 250 + y + 365 - 615 = 100x + y.

Hopefully it is easier to see now why you are left with a number that has your age as the first two digits and your house number as the last two. When you multiply a whole number by 100, the last two digits will be zero, so adding your age (provided you are under 100...) will not change the digits of your house number. Of course this only works if your house number is a 2 digit whole number. Sorry Sherlock, won't work for you.

2. If all the stars stand for the same number, can you complete: (*/*) - (*/6) = (*/12)?

* = 4.

Again, simple algebra will help out here. You know that */* = 1 no matter what * is, so you are left with:
1 - (*/6) = (*/12)
1 = (*/12) + (2*/12) = (3*/12) = (*/4)
So * = 1x4 = 4

3. If you start with the number 2 and stick an extra digit 1 at the beginning you get 12, which is exactly six times the number you started with.
Can you find a number so that when an extra digit 1 is written at the beginning you get 3 times the number you started with?
Can you find one so that the number you get is 5 times the number you started with?
Can you find one so that the number you get is 9 times the number you started with?

Again, there is more than one solution to some or all of these. Comment away!

(a) 5
(b) 25
(c) 125

4. In the multiplication 6 x 2 = 3 all the digits are correct, but they are in the wrong places. The equation should be 2 x 3 = 6 (or 3 x 2 = 6). In each of the next three multiplications all the digits are correct, but some of them are in the wrong places. Can you put them right?

28 x 1 = 44

43 x 2 = 14

76 x 8 = 41

There are (apparently, I haven't really had time to check) a few different answers to some of these. Here are the ones that the back of the book says. Feel free to comment any others that you find!

(a) 21 x 4 = 84
(b) 14 x 3 = 42
(c) 17 x 4 = 68

That's it for this week! See you again next Monday :)

Monday Maths Madness 24

I think it's time for some more puzzles. I got these ones out of a book called Mathematical Puzzling by A. Gardiner. I have no idea where this book came from. I think my mum gave it to me... Anyhoo! Puzzles :)

1. Take your house number and double it. Add 5. Multiply by 50. Then add your age, the number of days in the year, and subtract 615. The last two digits are your age, and the first two are your house number. Can you explain why?

2. If all the stars stand for the same number, can you complete: (*/*) - (*/6) = (*/12)?

3. If you start with the number 2 and stick an extra digit 1 at the beginning you get 12, which is exactly six times the number you started with.
Can you find a number so that when an extra digit 1 is written at the beginning you get 3 times the number you started with?
Can you find one so that the number you get is 5 times the number you started with?
Can you find one so that the number you get is 9 times the number you started with?

4. In the multiplication 6 x 2 = 3 all the digits are correct, but they are in the wrong places. The equation should be 2 x 3 = 6 (or 3 x 2 = 6). In each of the next three multiplications all the digits are correct, but some of them are in the wrong places. Can you put them right?

28 x 1 = 44

43 x 2 = 14

76 x 8 = 41

That's it for today. I'll try to get the answers out on Wednesday, but it may be later depending on how well my assignments go.

Monday Maths Madness 20 - Answers

As promised, here are the answers to Monday's puzzles.

1. Christmas Past, Christmas presents

Answer: On the 12th day alone, my true loves sends to me 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78 presents.

Over the duration of the 12 days, my true love sends to me 12 partridges in a pear tree, 11 lots of 2 turtle doves, 10 lots of 3 French hens, and so on. In other words (or numbers I suppose) I get 2 x ((1 x 12) + (2 x 11) + (3 x 10) + (4 x 9) + (5 x 8) + (6 x 7)) = 364 presents. Which is one for every day of the year except Christmas!

2. What to wear where

We know that Miss Black can't be wearing the black dress, but she also can't be wearing green, as the woman in green answered her. Therefore, Miss Black is wearing white, Miss Green is wearing black and Miss White is wearing green.

3. A toast to toast

First, toast one side of slices 1 and 2. Second, toast the other side of slice 1, and the first side of slice 3. Third, toast the second side of slice 2 and 3. Then you have toasted both sides of 3 slices in just three toastings.

Well done if you got the answers :)

Monday Maths Madness 20

Today is the last Monday of my first term at university. It has gone by so quickly, but I am ready to come home at the weekend. I keep counting down the days, I can't wait! In the meantime, I have run out of pictures, so I think it's time for more puzzles. These are from Ball of Confusion again.


As I am sat here learning Christmas songs for Glee club, I feel it is appropriate to start with a Christmas puzzle.

Christmas past, Christmas presents

On the first day of Christmas my true love sent to me, a partridge in a pear tree. That was 1 present, but on the second day of Christmas, my true love sent to me, 2 turtle doves and a partridge in a pear tree. That was 3 more presents - 4 in total. We know, of course, that this continued for the entire 12 days of Christmas.

How many presents arrived on the 12th day of Christmas? How many presents arrived over the entire 12 days?

What to wear where

Three girls turned up to a party in a black dress, a green dress and a white dress. They were Miss Black, Miss Green and Miss White. Miss Black said, "It's amazing - our dresses match our names, but none of us is actually wearing the dress that matches her name."

The girl in green said "So what?".

Who was wearing which dress?

A toast to toast

You only have a grill and space for two pieces of bread under it, so it takes 4 toastings to do 3 slices on both sides. Or does it?

Can you toast 3 pieces of bread on both sides in less than 4 toastings?

That's all from me this week. I would find more, but I have songs to practise. Answers on Wednesday!

Monday Maths Madness 12 (part 2)

As promised, here are the answers to the puzzles I gave on Monday.

1. Fumbling in the dark.

I would need to take 4 shoes to be sure of having a pair that match. If you took only 3 shoes, you could have taken one of each pair, so taking one more ensures you definitely have a pair of matching shoes.

Similarly, I would need to take 3 socks to be sure of having a pair that match.

2. Animal Farm

He would still have 50 horses - calling a cow a horse doesn't make it a horse.

3. Sum for simpletons

56 = 7 x 8

4. An up and down kind of existence

There is an absolute certainty that the monk will be at the same point on the road at the same time of day. Because the monk leaves later and arrives earlier on the second day than on the first day, there isn't a time of day on the second day that he was walking when he wouldn't have been on the first day. Therefore, if you imagine both journeys being made on the same day by two different monks, there comes a point where the two monks would have to walk past each other.

Monday Maths Madness 12

For anyone who is into Strictly Come Dancing, you will know that one of the celebrities is Johnny Ball. Johnny Ball is a TV personality from the 70s and 80s, and is known for popularising maths and science for children.

A little while ago, I can't remember exactly when, my mum bought me a book written by Johnny Ball. It is called Ball of Confusion, which is a collection of puzzles to do with maths, inspired by when he presented a puzzle on Zoe Ball's (his daughter) Radio 2 show. As Strictly just started this last weekend, I thought I would give a few puzzles from the book for you to ponder over.

1. Fumbling in the Dark

The lights have gone out - I said we should never trust wind farms - and I have to search my wardrobe in the dark for a pair of shoes and socks.

I have 3 pairs of shoes, 12 pairs of black and 12 pairs of brown socks.

How many of each do I need to take, to be sure I have a matching pair of each to wear?

2. Animal Farm

A farmer has 20 goats, 30 cows and 50 horses. How many horses would he have if you called the cows 'horses'?

3. Sum for simpletons

Look at this: 12 = 3 x 4.

Can you think of four other consecutive digits that do that?

4. An up and down kind of existence

A monk lives on a river bank in a valley. Once a week he must travel to the monastery at the top of the Lonely Mountain. He sets off at dawn, as the road is steep and long, and he arrives as the Sun sets. Next morning he has a lie in and leaves for home at 10am. As the road is downhill all the way, he arrives home at around 3pm.

What are the chances of the monk being at exactly the same point on the road, at exactly the same time on both days?

Answers on Wednesday! (Just to annoy my sister :P)