11 Days of Winter Break

Transcription

1 11 Days of Winter Break Advanced Learning Department Compiled by: Sam Nadolsky The following problems are intended for students in 3rd through 6th grades, although they can be fun for the whole family. Try to work on a problem a day to keep your student s mind active over the holiday break. To access the answers, head to our website at and go to the Links tab. Wishing you happy holidays and an enjoyable respite from school and work. 1. White, Black, and Brown Professor Merle White of the mathematics department, Professor Leslie Black of philosophy, and Jean Brown, a young stenographer who worked in the university s off of admissions, were lunching together. Isn t it remarkable, observed the lady, that our last names are Black, Brown, and White and that one of us has black hair, one brown hair, and one white? It is indeed, replied the person with black hair, and have you noticed that not one of us has hair that matches his or her name? By golly, you re right! exclaimed professor White. If the lady s hair isn t brown, what is the color of Professor Black s hair? Professor Black - White Hair Jean Brown - Black Hair Professor White - Brown Hair 2. Read the Hieroglyphics The seven symbols shown below look like some kind of ancient writing. But there is a meaning for each symbol, and if you can puzzle them out, you should have no trouble drawing in the square the next symbol of this curious sequence. If you draw a vertical line down the middle of the symbols, you ll see that each symbol is formed by the reflection of the numbers 1 through 7 across that vertical line. So, the final shape should look like 88

2 3. Big Cross-Out Swindle Cross out nine letters in such a way that the remaining letters spell a single word. N A I S N I E N L G E L T E T W E O R R S D If you cross out every other letter starting with the first letter, you will form A Single Word 4. The 4-Digit Multiplication Mystery A 4-digit number A B C D when multiplied by 4 gives another 4-digit number D C B A. What are the values of A, B, C, and D? Each digit is different and it can be any number from 0 to 9. A can only be 1 or 2. A=2, B=1, C=7, D=8 5. Four What Number Am I Riddles a. I am a number between 20 and 30, a multiple of 4 and also a multiple of b. I am a number between 30 and 40. I am a factor of c. I am an odd number smaller than 50 but greater than 30. I am a multiple of 7. I am not a multiple of d. I am a number greater than 10 but smaller than 40. I am a factor of 56 but not a multiple of How Many Apples? A grocer sold a carton of apples to some customers. The first customer tasted on apple and bought half of the remaining apples. The second and third customer did the same. The fourth customer bought the remaining 23 apples. How many apples were there in the carton at first? 191 Apples were first in the carton. The first customer tasted 1 apple, then bought half of the remaining 190 apples, leaving 95 apples. The second customer tasted 1 apple, then bought of half of the remaining 94 apples, leaving 47 apples. The third customer tasted 1 apple, then bought half of the remaining 46 apples. This leaves 23 apples for the 4th customer to buy.

3 7. A Weighty Problem Cylinder = 6 pounds Box = 2 pounds 8. Puzzling Polygons Same polygons stand for same digits. Different polygons stand for different digits. Find the value of each polygon.

4 9. Five 5 s Use five 5 s and any operations (add, subtract, multiply, divide, fractions, parentheses). Write a number sentences that equal each of the numbers from 1 through 9. Hint: see 10 and don t forget PEMDAS! ( ) 5 ( 5 5 ) = 1 ( ) 5 + ( 5 5 ) = 2 ( ) 5 + ( 5 5 ) = 3 ( 5 5 ) 5 ( 5 5 ) = 4 ( 5 5 ) 5 ( 5 5 ) = 5 ( 5 5 ) 5 + ( 5 5 ) = ( 5 5 ) + ( 5 5 ) = ( ) 5 = 8 ( ) = No Repeats! I just promised to help out at the library every day after school. Going the same way can get boring, so I d like to try a different 6-block route each day. For how many days can I go from school to the library without repeating a route? 20 Routes

5 11. Magic Shapes These shapes rely on overlapping number relationships for their unusual qualities: For the magic triangle, arrange the numbers 4 through 9 in the circles so that every side of the triangle equals 21. For the magic daisy, place the numbers 1 through 11 in the circles so that every straight line in three circles totals 18. For the magic star, place the numbers 1 through 12 in the circles so that each straight row of four circles adds up to 26. In this case, you may find more than one solution.

6 Problem Credits: 1. My Best Mathematical and Logic Puzzles - Martin Gardner 2. My Best Mathematical and Logic Puzzles - Martin Gardner 3. My Best Mathematical and Logic Puzzles - Martin Gardner 4. Singapore Math 5. Singapore Math 6. Singapore Math 7. Awesome Math Problems for Creative Thinking - Greenes, Findell, Gavin, Sheffield 8. Awesome Math Problems for Creative Thinking - Greenes, Findell, Gavin, Sheffield 9. Awesome Math Problems for Creative Thinking - Greenes, Findell, Gavin, Sheffield 10. Awesome Math Problems for Creative Thinking - Greenes, Findell, Gavin, Sheffield 11. Challenging Math Puzzles - Glen Vecchione