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The Least Greatest Number

What is the units digit of the least whole number greater than 1000 whose digits are all different?  And what is the number it self?

The answer is 3. The first digit has to be 1, the second has to be 0, then the third is 2, and finally 3. So the number is 1023.

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Apple Pie

Billy cut an apple pie into equal pieces. He ate two pieces, and his brother ate one.  Their mom walked in and said, "Wow! You guys have eaten half the pie!"  Into how many equal pieces had Billy cut the pie?

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The answer is 6 pieces.

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Tick Marks on a Ruler

How many tick marks are needed to create a ruler that is 9 inches long, if a tick mark is used every quarter inch?

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The answer is 37.... don't forget the very first one used to mark zero (0).  9 x 4 is 36 plus one is 37. 

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Whose number is greatest???

    Jose, Thuy, and Kareem each start with the number 10.  Jose subtracts1 from the number 10, doubles his answer, and then adds 2.  Thuy doubles the number 10 subtracts 1 from her answer, and then adds 2.  Kareem subtracts 1 from the number 10, adds 2 to his answer, and then doubles the results.  Who gets the largest final answer?

Answer: Kareem has the largest final answer.  Jose gets 2(10-1) + 2, or 20.  Thuygets 2(10) - 1 +2, or 21.   Kareem gets 2(10 -1 + 2), or 22.

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Powers of Ten

Since we are studying powers of ten I'd like to know the names of the some of them...    So give the names of these:

ten to the fifth: ______________ Give me the full name of the largest named number: _______________________________
1010: ______________
1015: ______________ And the power below it: ________________________________



ten to the fifth: hundred thousand Give me the full name of the largest named number: __agoogleplex__(a one followed by a googol zeros)
1010: ten billilon
1015: quadrillion And the power below it: This is not found on the internet nor any books I have looked in so... it will be extra credit (5 points) to anyone who does find it.

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Denominatior of 23????

How many fractins with a denominator of 23 have values between 0.18 and 0.82?

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Answer: 14 fractions.  4/23 has a decimal value of approximately 0.174, which is too low; therefore, 5/23 is the first fraction within the interval.   The fraction 19/23 has the decimal approximation of 0.826, which is too large: therefore, 18/23 is the last fraction in the interval.  So 18 - 5  + 1 is 14.  

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What's the remainder??

    Without using a calculator,  figure out what is the remainder of the product (1492)(1776)(1812)(1999) when it is divided by 5. {in other words when the four numbers above are multiplied together and the answer is divided by 5 what would the remainder be??} You must send an explanation of how you figured this out to get credit.

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Answer: The trick to this one is:  Just multiply the last digits together.  2 x 6 x 2 x 9 to get your anwer... this equals 216 then just look at the last digit here.  It is a 6 so 5 goes in to it only once with a remainder of 1. 

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A Family of Water Drinkers

A mother drinks eight 8-ounce glassses of filtered water a day, a father drinks five 8-ounce glasses a day, and their child drinks four 8-ounce glasses a day.  If they change their filter every 60 gallons, how many days will each filter last??

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Answer: The filter lasts about 56 1/2 days.  The family consumes 17 glasses, or 136 ounces, of water each day.   One gallon is 128 ounces, so 136 128 is 1.0625, or 1 1/16, gallons a day; 60 gallons 1.0625 gallons/day is about 56.5 days.

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The Volunteers

You sign up to do volunteer work every fourth Sunday of each month at a soup kitchen for the homeless.  On what dates of the month might the fourth Sunday fall?

January 19....
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30

Extra, Extra Credit.... what is the calendar saying? and why is it significant to me????

Answer:  Days 22 - 28. The first Sunday must fall in the first 7 days.  If the first Sunday is on the first, then the fourth Sunday must be the 22nd.  If it falls on the 7th day then the fourth Sunday is on the 28th.

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The One Week Stay

    Assuming that all other things are equivalent, which is a better deal: a one-week stay at a camp that costs $105 per day plus a 15% processing fee or a one-week stay at a camp that charges a flat rate of $120 per day?

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Answer: The flat rate is a better deal.  The total cost for the first camp is $105 x 7 x 1.15 = $845.25.   The Second camp's cost is $120 x 7 = $840.

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Squared Rectangle

A square and a rectangle have the same area.  If the perimeter of the square is 24 inches, and the width of the rectangle is 3 inches, what is the perimeter of the rectangle?

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Answer:  30 inches.  A square with a perimeter of 24 inches has sides of 6in and an area of 36 square inches.  the rectangle having the same area of 36 square inches with one side being 3 inches would have the other side with a length of 12 inches.  (So the perimeter woould be  3 + 3 + 12 + 12 , or 30 inches.

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Page by: Mathman (Bruce A. Titen) 1998

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