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 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 :)

The Dominoes and the Chessboard

On Monday, I posted a puzzle regarding a chessboard and some dominoes. As promised, I am now going to give the answer (so that my boyfriend's family will stop arguing about it!)

So, is it possible to place 32 dominoes, each covering two squares, on a chessboard with two diagonally opposite corners cut out?

The answer is: No. It is not possible.

But how do you prove it? Most of the modules in my degree this term are all about proving things, and it can get very confusing. Especially Analysis. But there is a simple way to think about this puzzle.

As the two corners cut out of the chessboard are diagonally opposite each other, they must be the same colour. This means that we have 30 of one colour (in the picture above it is black) and 32 of the other colour (obviously, in this case white). As the dominoes only cover two squares, no matter how you place them, they are going to cover one of each colour. So if we pair off the colours, we can match 30 black to 30 white, but then we are left with 2 of the same colour left over. We know that a single domino cannot cover two squares of the same colour, so the puzzle is therefore impossible.

Hopefully I explained that clearly so you aren't left feeling as confused as before!

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.