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A Beer Trick

By on 01/02/2016

The trick is performed by a (mathe)magician with a participator. In the following dialogue, the mathemagician’s text is printed in Roman, and the participator’s in Italics. If you do not know the trick, I encourage you to take the participators part and perform his actions as you read down the dialogue…

A calculating conversation

How many of your favourite drinks do you approximately drink every day? Don’t tell me, but remember the number, or write it down.
Hmm… [thinking: 4; you, the reader, are free to choose your number (it should be a nonnegative integer ;-)) here and perform the following calculations with it…]

Today it is very hot, so you are very thirsty. You drink twice your average, so multiply your number with 2.
[2 ⋅ 4 = 8]. Did it. What next?

You are walking down the street and meet a friend you haven’t seen for a long time. He invites you to go with him to a bar and you accept. You have much to talk about, and as the time passes, you have drunk 5 more of your favourite drinks, so add 5 to your last number.
[8 + 5 = 13]. Err, I think this it too much for me.

Don’t worry, I don’t expect you to drink that much. At least not right away… As the obtained number is obviously much above your daily average, we’ll take it as an approximation of your weekly consumption. In fact, I’m more interested in finding estimates of how many of their favourite drinks people drink yearly. The year has 52 weeks, but as I’m only interested in estimates, it is enough if you multiply your last number with 50.
[50 ⋅ 13 = 650] Did it. Do you wan’t to know the result?

No. [650 + 1760 = 2410]

Now, for your last exercise in arithmetics, subtract the year of your birth from the previous result. The full four-digit year, please. Tell me the result when you’re done.
[I’m born in 1971, so 2410 – 1971 = 439] My final result is 439.

You are 39 [the last two digits] years old and drink 4 [the number obtained removing the last two digits of the result] of your favourite drinks daily!

How the mathematician becomes a mind-reader…

The explanation of the trick is simple algebra of the level everybody learns in school. If you, the reader, are a mathematics teacher, you can easily make your students discover the following explanation, or parts of it (e.g.how the number to be added before subtracting the year of the birth depends on the calendar year in which the trick is performed) themselves. The explanation is as follows:

If m is the daily number of drinks, the first part of the trick calculates first 2m, then 2m + 5, and then (2m + 5)⋅ 50 = 100m + 250. By adding a number k and subtracting the birth-year n we obtain the final score 100m + 250 + kn. Since multiplying by 100 “moves” m two digits to the left (many simple mathemagical tricks are based on this simple fact, and use sequential calculations to hide the principle!), in order to have the last two digits represent the age of the person, we must have “age” = 250 + kn. Since “age” = “this year” – n if the birthday already passed, we obtain k = “this year” – 250 (so, in 2011 k = 1761). If the birthday hasn’t passed yet, obviously k has to be one less (1760 in year 2011).

Important note: If you will present this trick in 2012, you will have to work with the number 1762 and 1761 (instead of 1761 and 1760); in 2013 with 1763 and 1762, etc.