Quiz 3 (Solution),
HW10, HW9,
HW8,
HW7
Des Chiffres et des Lettres:
This is a very popular afternoon TV gameshow in France, comparable in
popularity to Jeopardy in the US. Two contestants battle it out with
letters and numbers. In the 'numbers' part of the show, one contestant
draws 6 cards with whole numbers on it, say 4,10,6,10,4,6. Then a slot
machine with three slots is run and a 3-digit number comes out, say
321. The contestants have 1 minute to come as close to 321 as possible
using the usual operations of arithmetic. They can put parenthesis
wherever they want, but each one of the 6 numbers given can be used
only once, and only whole numbers should be involved. Try it! (There is
a way to get the exact number).
Mental Math Tags:
11^2=121, 12^2=144, 13^2=169, 14^2=196, 15^2=225, 16^2=256, 17^2=289,
18^2=324, 19^2=361
2^5=32, 2^8=256, 2^10=1024
HW4,
HW5,
HW6,
Quiz2
HW1, HW2, HW3, Quiz1
The Pennies Game:
Make three piles of pennies, say 10,5,7. Take turns choosing a pile
and removing as many penny as you wish from that chosen pile. The
person who removes the last pennies wins. There is a winning strategy
based on base 2. The goal when it is your turn is to reestablish a
certain symmetry. So say you are going first and the piles have 10,5,7
pennies respectively. Convert to base 2: you get 1010, 101, 111. Now
look at each denomination, for instance the 'ones': the first pile has
no ones, while the other two piles do, this is good, you either want
no piles to have a certain denomination or two piles to have it. So
let's look at the next denomination, the 'twos': the first and third
pile have twos, but the second pile doesn't. That's good also. So
let's look at the 'fours': the second and third pile have fours, but
the first pile doesn't: that's good again. Finally, look at the
'eights', only the first pile has an eight. This is not good, to
reestablish the symmetry you need to choose the first pile and remove 8 pennies
from it.
Averaging Mentally:
Given some numbers that are fairly close together, say 1142,1147,1143
you can use the following strategy: first find the greatest multiple
of ten which is smaller than the numbers you are given: in our example
1140, then average the errors, namely 2,7,3, you get 12/3=4, so add 4
to 1140, and you get 1144. Notice that chosing a different number than
1140 would have yielded the same answer (try 1141 instead). You can
even guess the average at first and use negative numbers.
Computing Tips Mentally:
Say you want to compute the tip (15%) on 36 dollars, first divide by
2, and get 18, then add this to 36 and get 54. Now read this number
starting with dimes, then dollars as denominations: 5 dollars and 4 dimes.
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