## Thursday, October 7, 2010

### If you don't want to guess, work it out in your head

Perhaps you have heard of the term math prodigy. Or math savant. Or mental calculator. Or mentat.

Are you one?  To find out, you could download the 2010 World Cup of Math material to practice on.

But first, I'll save you some effort. Get the material only if you can solve all these sorts of problems in your head:
1. calculate the number of days between each pair of 50 pairs of dates
2. subtract 10 pairs of 8-digit numbers
3. add 10 sets of ten 10-digit numbers
4. calculate the square roots of ten 6-digit numbers
5. solve 27 multiplication and addition problems involving 8-digit numbers
6. calculate cube root, fourth root and fifth root of three 6-digit numbers
7. solve some algebraic calculations
8. look at 20 different 5-digit numbers and identify two prime factors for each
9. solve a multiplication problem involving a fraction, pi and a decimal number cubed
10. look at 20 different addition or subtraction problems involving 2 or 3 digit fractions, then decide if the sum or remainder of the problem is greater than, equal to, or less than another integer

You may be able to do some of them in your head, some on paper, some with a calculator, etc.

But to give you an example of a mental calculator's ability, let's take one of the 50 sets of dates in Example 1.

I'll give you two dates and you tell me the number of days between those two dates. Ready? Go!

23 July 1962 to 05 August 2026

My Guess
Mentally I see it's 64 years, 13 days which is about 22,000 days. That's my guess and I'm sticking with it. I guess I'm too lazy to try harder.

My calculator says the real answer is 23,389 = (((64 x 365 + (64/4)) + 13)  so I was only 10% off or so!

Mental Calculator
The mental calculator winner this year, Yusnier Viera, was able (in his head) to determine 48 of the 50 answers correctly in one (1) minute!

Momma mia!

For the rules on how to compete, read on:

Witnesses
Record attempts have to take place in public (university, school or museum). Two witnesses must confirm the record and at least one must have a professional background in mathematics.

Presentation of the Problem
Calculations can be done with the problem in sight. The mental calculator can dictate, write or type the answer but is not allowed to write down intermediate results.

Number of Attempts
Only 10 record attempts may be made within a period of 24 hours. The calculator should clearly say when he or she stops practicing. The witnesses may then signal the start of an official record attempt.

Timekeeping
Timing begins when the task is shown to the competitor and ends at the end of writing/dictating the answer. Two stop watches should be used. At the end of the attempt, average the two watches.

Computer Use
A computer program may show the tasks on the screen, let the calculator type an answer, compare the results and measure the time until the last keystroke. Correcting while still typing is allowed, but if the computer says a result is wrong, no correction is allowed. Attempts must still be in public and witnessed by two persons.