Lemon Squares

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It’s December, and that means baking season begins! I don’t have the original source for this one, but everyone seems to really love these lemon squares. As such, they’re are quickly becoming my de facto treat for the holidays.

Bottom Layer:
1 cup butter
2 cups flour
1/2 cup icing sugar

Whisk the flour and icing sugar until nicely mixed and then gently beat in the softened butter with a fork. This should result in a nice crumbly short bread base. Press into a parchment lined pan and bake @ 350 for 20 minutes.

Top Layer:
4 eggs beaten slightly
2 cups white sugar
6 tbsp flour
6 tbsp lemon juice
1 tbsp lemon rind (pack it just a bit to get extra in :) )

Pour over crust and bake @ 350 for 25 – 30 minutes. Remove from oven and sift some additional icing sugar on top.

Smoothie

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For the past few months I’ve been loving making smoothies. They’re a healthy, nutritious, and tasty treat that can easily be changed up with different fruit combinations. I thought since I’ve sort of come up with my de facto smoothie I’d post it here for others to enjoy. Unfortunately, I don’t really measure anything, just kind of go by feel after making so many. That being said, I’ll try to approximate things but I encourage you to play around with the measurements and find one that works best for you.

  • half a Banana
  • about one cup of frozen berries (blueberry, blackberry, raspberry, strawberry)
  • two to three spoons of vanilla yogurt (this is my one “bad” ingredient [high sugar content], I should really be using plain yogurt)
  • some cinnamon (half a teaspoon or less)
  • some honey (no clue, just squeeze some in)
  • some flax seed (about 3/4 tablespoon)
  • milk (little for thick smoothie, lots for runny smoothie)

Why consumers should purchase business-class laptops

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I’ve long been a fan of the IBM/Lenovo Thinkpad T-series laptops. They are powerful, durable, and have the greatest keyboard of any laptop I have ever used. As a general “techie” guy, I’m often engaged for purchasing advice by friends or family members when buying electronics. Recently, my sister-in-law decided to buy a laptop and approached me regarding options. I sent her a rather lengthy email outlining the reason why I believe it was in her best interest to buy a business-class laptop and I will reiterate some of that email here:

Basically, this is what I think a business laptop offers over a consumer device (for the 30-40% $$ premium):

  • Far superior build quality. Metal hinges, roll cages, higher quality plastics, etc. This means the laptop will last longer (3 – 5 years as opposed to the 2 – 3 years you’ll get out of a consumer laptop).
  • Smaller but faster hard drive. Consumer hard drives are typically very large (500 – 750 GB) but slow (5400 RPM) whereas business hard drives are small(er) (320 GB) but fast (7200 RPM). Realistically, no one needs 500+ gigabytes of local storage on their laptop. Heck, my network drive is chaulk full of media content and it hasn’t even come close to hitting 500 GB yet.
  • Less RAM. Again, consumer laptops seem to come jammed with tons of RAM (8 GB), business laptops tend to have 2 – 4 GB. At the end of the day, you don’t need more than 4 GB, plus, it’s dirt cheap to buy if you do (I just bought 4 GB for $30).
  • Better battery life. Consumer laptops are terrible on battery drain – often only getting 3 – 4 hours on a full charge. My Lenovo T400 got 7 hours out of a charge when new and even now, three years later, I still get 3 – 4 hours out of it. Be wary that manufacturers often advertise the cells (typically 6-cell), but not the capacity (mAh).
  • Better keyboard. To me, this is the #1 reason to buy a business laptop. The keyboard is the one part of a laptop you will use more often than any other peripheral so you want one that is good. A business-grade keyboard will be spill-resistant, have low flex, good response, and long life (keys won’t go soft or flaky after a year of use).
  • Screen resolution. Consumer laptops are currently all 720p (1366×768). This may be fine for multimedia but it is (in my mind) unacceptable for virtually everything else (web surfing, document or image editing, programming, gaming). Business laptops are customizable and offer numerous resolutions.
  • Matte screens. My god people, why are you encouraging manufactures to keep cranking out these awful high-gloss screens. Virtually all consumer laptops sold today have high-gloss screens that are highly reflective and show everything (fingerprints and your reflection) except the content on the screen!. If your intent is to use your laptop as a mirror, then by all means go with the high-gloss screen, but if you actually want to do anything useful with your device, you need a matte screen.

If you require further convincing, here is another article on the subject http://blog.laptopmag.com/10-reasons-why-consumers-should-buy-business-notebooks

With that being said, not everyone can afford to fork out $1000+ for a nice new Lenovo T520 (or other reputable business laptop), as was the case with my sister-in-law. Luckily, many manufacturers such as Lenovo and HP are offering entry level business laptops as a price competitive with consumer laptops ($600). Try checking out Lenovo, HP, and Dell for their entry-level business offerings.

If at this point you are still not convinced of the merits of buying a business laptop, then at least consider the following when buying a consumer grade laptop:

  • Keyboard. As I said before, this is the most important part of a laptop purchase – don’t get caught up in the massive hard drive size or large RAM that the sales associate will try to sell you on (they know all consumer laptops are basically the same!). Any time you look at a laptop in store, do yourself a favour and type on the keyboard. You need to find one that feels right for you.
  • Screen size. Bigger screen = larger and heavier device. Do you want small but light and mobile or are you going for big but heavy and stationary (i.e. desktop replacement). The happy medium seems to be 15.6″.
  • Graphics. Try not to get sucked into paying for a dedicated graphics card. At the end of the day, if you want your laptop to be a gaming machine, then you definitely don’t want to be buying a consumer laptop. For gaming laptops check out some premium manufacturers such as Alienware, iBUYPOWER, Falcon Northwest, Sager, etc. For your every day consumer stick to the onboard graphics (Intel HD 3000 as of this writing).

One final thought: please keep in mind that price does not necessarily buy power, it buys longevity. Paying a premium for a business-grade laptop gets you the materials and design to keep the laptop in good condition for a long period of time.

Problem Solving: Apples, Oranges, and Mixture

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You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. However, each of these labels is always placed incorrectly. How would you pick only one fruit from a basket to place the labels correctly on all the baskets? (Source: My Tech Interviews)

Select from the mixture, if you got an apple then you know:

  • basket mixture should be labelled as apples (we know the label mixture is incorrect so it must be apples since we pulled an apple)
  • basket oranges should be labelled mixture (we know the label oranges is incorrect and apples was just labelled)
  • basket apples should be labelled oranges (only one left)

In a similar vein, if you got an orange from the mixture basket then:

  • basket mixture should be labelled as oranges
  • basket apples should be labelled mixture
  • basket oranges should be labelled apples

Problem Solving: Music Society Attendance

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The local Music Society had their fall concert last night. Ticket prices were as follows: men $5 dollars, women $2, children 10 cents. Coincidentally, 120 people attended and $120 was earned from ticket sales. How many men, women and children were in attendance? (Source: A Daily Brain Teaser)

Well, on initial investigation I see two equations and three unknowns.
Let x represent the number of men in attendance
Let y represent the number of women in attendance
Let z represent the number of children in attendance
The two equations are as follows:
a) 5x+2y+0.1z=120
b) x+y+z=120

The problem now is that I need a third equation to solve for all three unknowns. Since I can’t come up with one, I’m going to have to resort to brute forcing this :( . Since we know the number of men can’t be greater than 24 (since 24\times5=120) we’ll start there and work down. I’ll use a table to check combinations of x, y, and z that work for equation a) and stop when I have a combination that also works for equation b).

x 24 23 23 22 22 22 22 22 22 21
y 0 2 1 5 4 3 2 1 0 7
z 0 10 30 0 20 40 60 80 100 10
x 21 21 21 21 21 20 20 20 20 20
y 6 5 4 3 2 10 9 8 7 6
z 30 50 70 90 110 0 20 40 60 80
x 20 19 19 19 19 19 19 18 18 18
y 5 12 11 10 9 8 7 15 14 13
z 100 10 30 50 70 90 110 0 20 40
x 18 18 18 17 17 17 17 17
y 12 11 10 17 16 15 14 13
z 60 80 100 10 30 50 70 90

Finally, we have a combination (17,13,90) that is valid for both equations. Thus, 17 men, 13 women, and 90 children attended the concert. It’s not pretty, but at least the problem is solved.

Problem Solving: Age of Freddie’s Parents

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Soon little Freddie will celebrate his tenth birthday. In 11 years Freddie will reach half the average age of his parents. His mother is only 17 years older than her son. How old are Freddie’s father and mother. (Source: A Daily Brain Teaser)

Since Freddie is currently 9 years old, in 11 years he will be 20. We know his mother is 17 years older than him so in 11 years she will be 37. Thus, we only have to solve for x, the father’s age in 11 years.
20=\frac{1}{2}((37+x)\div2)
40=(37+x)\div2
80=37+x
43=x

So, in 11 years Freddie’s mother will be 37 and his father will be 43. Thus, Freddie’s mother and father are 26 and 32, respectively.

Problem Solving: Encryption (I)

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If 8-22-5-22-13 equates to seven and 7-4-12 makes two, how would you write ten? (source A Daily Brain Teaser)

This is a simple one-to-one letter substitution. You can see that “seven” is represented by five letters, and “two” by three letters. Furthermore, the letter “e” in “seven” is coded as 22 consistently. Quickly reviewing the mapping, it’s easy to see that the letters are coded from 1 – 26 (Z to A). Thus, “ten” would be written 7-22-13.

Problem Solving: Jam eating contest

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At the recent inter-departmental jam making contest, four lucky candidates took part to make the juiciest strawberry jam. The ages of the contestants were 14, 17, 20 and 22. As it happens the person who came last was the oldest, whereas Stuart was three years older than the person who came second. James was neither the oldest nor the youngest and Kev finished ahead of the 17 year old, but didn’t win. John was also unlucky this time and didn’t win either. Can you determine who finished where and how old they are? (Source: A Daily Brain Teaser)

This sets up nicely for a process of elimination. We’ll begin with a table of all possibilities and then remove items based on knoweledge gained (i.e. logical deduction).

14 17 20 22
first J Ja K S J Ja K S J Ja K S J Ja K S
second J Ja K S J Ja K S J Ja K S J Ja K S
third J Ja K S J Ja K S J Ja K S J Ja K S
last J Ja K S J Ja K S J Ja K S J Ja K S

To begin, we know that the oldest person ended up in last, so we can eliminate all from (1,4),(2,4),(3,4),(4,1),(4,2),(4,3)

14 17 20 22
first J Ja K S J Ja K S J Ja K S
second J Ja K S J Ja K S J Ja K S
third J Ja K S J Ja K S J Ja K S
last J Ja K S

Furthermore, we know that Kevin did not win (eliminating him from (1,1),(1,2),(1,3)), but also that he placed higher than the 17 year old. Since we know the 17 year old did not place last, then he (the 17 year old) must have placed at least third, meaning Kevin must have placed second (eliminting him from (3,1),(3,2),(3,3),(4,4))

14 17 20 22
first J Ja S J Ja S J Ja S
second J Ja K S J Ja K S J Ja K S
third J Ja S J Ja S J Ja S
last J Ja S

Now, we’ll knock off four at once here. First, we know James is neither the oldest nor the youngest so he can be eliminated from (1,1),(2,1),(3,1),(4,4). We also know that Stuart is three years older than the second place contestant. Since only the 17 year old and 20 year old are three years older than another contestent, Stuart must also not be the oldest or youngest so he too can be eliminated from (1,1),(2,1),(3,1),(4,4). Now, you’ll notice only John remains in (4,4) so clearly he is the 20 year old who finished in last and can thusly be eliminated from the rest of the table. Notice also that we have proved that James and Stuart must be the middle aged persons so Keven must be 14.

14 17 20 22
first Ja S Ja S
second Kevin Ja S Ja S
third Ja S Ja S
last John

Finally, since we know Stuart is three years older than the second place contestant, and Kevin finished second, Stuart must be 17, leaving only James for the 20 year old. To complete the solution, we know that Kevin finished higher than the 17 year old, so Stuart must have finished third, leaving James as the first place contestant.

14 17 20 22
first James
second Kevin
third Stuart
last John

Problem Solving: Complete the sequence (II)

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Two years ago, a man was offered a motorcycle for $1024, but he declined to buy it. A year later, he was offered the same motorcycle for $640, but again decided not to buy it. A little while after that, he was again offered the motorcycle, this time at $400. Again, he refused to buy it. Last week, he turned the motorcycle down even though the price had now fallen to $250. If the owner offers it for sale yet again, and he makes a consistent reduction, how much will it be for sale for the next time? (Source: A Daily Brain Teaser)

$156.25
Each offer made was exactly 37.5% lower than the previous one. Since 37.5% of 250 is 93.75, the next offer will be 250 – 93.72 = 156.25.

Problem Solving: Complete the sequence (I)

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What comes next in the following sequence: 1,11,21,1211,?

111221
This is a pair sequence where the first digit of each pair specifies how many of the second digit occurred consecutively in order in the previous sequence value. So, after starting with 1, the second value is 11 because we had one 1 in the first value, then 21 because we had two 1′s in the second value, then 1211 because we had one 2 and one 1 in the third value, and finally 111221 because we had one 1, one 2, and two 1′s in the fourth value.