Elementary POW, December 11-15, 1995
Elementary POW Problems || October-December, 1995 Problems || Elementary POW Main Page
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Elementary Problem of the Week, December 11-15, 1995
This week's problem was submitted by Nicole Adams,Grade 12, Mount St.
Joseph Academy, Flourtown, PA.
Arrange all the integers from 1 to 9 in such a way that the numbers total
100 exactly. Here's an example:
12 + 3 + 4 + 5 - 6 - 7 + 89 = 100
You don't have to keep the numbers in order and you can use any operations
to get your answer. Here's another example:
98 3/6 + 1 27/54 = 100
How many combinations can you find?
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This week's Bonus Puzzler is called, O Tannenbaum, by David Tuller and
comes from Games Magazine. Place each of the numbers from 1 to 10 in the
ornaments below so that every dashed line adds up to the same number. Two
numbers have been given to start you off. The answer is unique.
___
| |
|___|
/ \
___ ___
| | | |
|_8_| --- |___|
/ \
___ ___ ___
| | | | | |
|___|--- |___| --- |___|
/ \
___ ___ ___ ___
| | | | | | | |
|___|--- |___|--- |_9_|---|___|
*Note: You should use a monospaced font such as "courier" when copying the
above diagram.
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Correct Solutions submitted by:
I'd like to give special recognition to the MATHFROGS:
RACHEL--NIKKI--STEVE--JOE--EVAN from Heights Elementary School, Sharon,
Mass., in Mr. Philips 6th grade class. They came up with 23 different
equations.
Matt Burke & Anita Minakyan at Munsey Park School Manhasset N.Y, in Mrs.
Hirns fourth grade class wrote one equation and gave 18 different
rearrangements of it.
Lisa Simmons, I.H.M. School, Phila., Pa, Gr. 6 was one of the few students
to use division in her equations.
Great work! I'm looking forward to a new year filled with challenging
problems.
**********************
Heights Elementary School
Sharon, Mass.
Mr. Philips
Grade 6
MATHFROGS: RACHEL--NIKKI--STEVE--JOE--EVAN (23 equations);
MATHSHARKS: Mark--Nicole--Erika--Liz--Adam (4 equations);
MATHMASTERS: Jackie-Tom- David- Robert- Rachel (5 equations);
MATHMACHINE: JAMIE--MIKE--KAYLA--MATT--EVIN (1 equation & Bonus);
MATHDRAGONS: Lia- Rabia- Natalie- Steve- Shyam (2 equations)
******************
The Bagnall School, Groveland, MA
Ms. Hilary Seager, Grade 4
Students: Mike D., Julia C., and Nick S. (Bonus), Meghan R. (Bonus)
************
Springton Lake
Pat Hagan's Sixth Grade class tions),
Students: Bill Van Ess (3 equations),Sarah Shahadi (1 equation), Mike
Scheuftan (2 equations), Travis Moore (2 equations), Rob Le Pard (1
equation), Vic Ruggiere (1 equation), Pierce Bolton (1 equation).
***********
School of the Holy Child, Drexel Hill, PA
Ms Caroline Brennan - Grade 6
Students: Kim Fugok, Christine McGowan, Ryan Grace, and Amanda Tumminelli
(3 equations)
***************
Joyce Kilmer School
Mrs. Bach - 5th Grade
Mahwah, NJ 07430
Joe Baxley (7 equations), Jessica Terry (1 equation), Jessica Kreusch (2
equations), Carolyn Weiss (1 equation), Jessica Ross (1 equation), George
Remo (1 equation), Amy Killough (1 equation), Jessica Cohen (1 equation),
Jenna Beatrice (1 equation), Carolyn Weiss (1 equation).
Bonus: Solved by Miguel Bayona and Leigh Ann Merkley
****************
Lisa Simmons, I.H.M. School, Phila., Pa, Gr. 6
(4 equations & Bonus)
************
Munsey Park School, Manhasset N.Y. 11030__
Mrs. Hirns fourth grade
Matt Burke & Anita Minakyan (1 equation - 18 rearrangements)
********************
Munsey Park School, Manhasset N.Y. 11030__
Mrs. Hirns fourth grade
Willam Lopez, Danny Maimone, Matt Horne, Anthony Figlia and Todd Conis and
Elizabeth Povlovitch. (1 equation)
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St. Mary's School
Ticonderoaga, NY
Emily Hoops of Grade 5 (1 equation - 13 rearrangements)
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Center School
Stow, MA
Ms. McCarthy's 4th grade
Chaz Rosenberg (3 equations & Bonus), Sam Hahn (Bonus)
Mrs. Trudell's 3rd grade class
Katie Stefanis (Bonus), Chris Balin (1 equation)
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Mrs. Perreault's Grade 4
Heights Elementary School
Mr. Philips
Grade 6
MATHFROGS: RACHEL--NIKKI--STEVE--JOE--EVAN
Solutions for the week of December 11-15.
1. 9 x 8 +7+6+5+4+3+2+1=100
2. 91+23+45+8-67=100
3. 25 x 4+9+8-3-6-7-1=100
4. 72+68-45+9-3-1=100
5. 93+7+8-6+5-4-2-1=100
6. 89+67-54-3+2-1=100
7. 87+69-54-3+2-1=100
8. 89+74-65+3-2+1=100
9. 89+75-64+3-2-1=100
10. 89+75-64-3+2+1=100
11. 89+73-65+4-2+1=100
12. 89+71-65+4+3-2=100
13. 89+76-53-14+2=100
14. 89+72-54-13+6=100
15. 89+64-57+3+2-1=100
16. 89+63-57+4+2-1=100
17. 89+62-57+3+4-1=100
18. 89+57-46+3-2-1=100
19. 89+57-46-3+2+1=100
20. 89+56-47+3-2+1=100
21. 89+53-47+6-2+1=100
22. 89+51-47+6+3-2=100
23. 89+46-37+5-2-1=00
MATHSHARKS: Mark--Nicole--Erika--Liz--Adam
Solutions for the week of December 11-15
1. 145-23+76-98=100
2. 9 x 8 +1+2+3+4+5+6+7=100
3. 89+5+3-7-6+12+4=100
4. 98+3+54-62+7 x1=100
We used trial and error to find our solutions.
We could not solve the bonus problem.
MATHMASTERS: Jackie-Tom- David- Robert- Rachel
Solutions for the week of December 11-15
1. 9x8+7+6+5+4+3+2+1=100
2. 42+58+7+6-9-3-1=100
3. 31+69+8+5-7-4-2=100
4. 21+79+6+4+3-5-8=100
5. 97+3-6+8-2-5+4+1=100
We used trial and error to reach our solutions.
We could not solve the bonus problem
MATHMACHINE: JAMIE--MIKE--KAYLA--MATT--EVIN
Solutions for the week of December 11-15
1. 9 x 8 +7+6+5+4+3+2+1= 100
Solution to the bonus problem:
1
8 10
6 7 5
3 4 9 2
Both problems were solved by the trial and error method.
MATHDRAGONS: Lia- Rabia- Natalie- Steve- Shyam
Solutions for the week of December 11-15
1. 89+5+3-7-6+12+4=100
2. 98+3+54-62+7 x 1=100
We used trial and error to reach our solutions
We could not solve the bonus problem.
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>Hi Ruth, This is from Pat Hagan's sixth grade class at the Springton Lake
Middle School in Media, PA. We had fun with this one. The students had half
of a class period and one night to come up with as many solutions as they
could. It was strictly trial and error.
Sarah Shahadi came up with the first solution after about 5 minutes:
67 + 54 - 23 + 9 - 8 + 1 = 100
Bill Van Ess was the only other student to come up with a solution in
class. Then he found 2 more for homework.
98 + 7 - 5 + 6 - 3 - 4 + 2 - 1 = 100
(89 + 7 + 4 + 6 - 5 - 3 + 2) x 1 = 100
(58 x 4) - 97 - 36 + 2 - 1 = 100
Mike Schueftan came up with two solutions for homework, also.
(56 + 34 - 8 + 9 + 7 + 2) x 1 = 100
(98 + 76)/2 + 3 + 4 + 5 + 1 = 100
Travis Moore found this solution for homework.
98 + 2 - 7 - 6 + 5 +3 + 4 + 1 = 100
Rob Le Pard found this solution.
78 x 2 - 45 - 6 - 9 + 1 + 3 = 100
Vic Ruggiere came up with this answer.
(84 + 3 + 2 - 5 + 7 + 9)x 1 = 100
And, finally, Pearce Bolton shared this solution.
12 x 6 + 3 + 5 + 7 + 8 + 9 - 4 = 100
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Grade 6
Students: Kim Fugok, Christine McGowan, Ryan Grace, and Amanda Tumminelli
Drexel Hill School of the Holy Child, Drexel Hill, PA Caroline Brennan
We tried for about 1/2 hour to find solutions by using a trial and error
method. This was harder than we thought. We listed our three solutions
below.
9 x 8 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 100
1 x (9 x 5) + 78 - 46 + 23 = 100
1 x ( 7 x 8) + (9 x 5) + 3 + 4 - 6 - 2 = 100
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Lisa Simmons, I.H.M. School, Phila., Pa, Gr. 6
The question was to arrange all of the nembers from one to nine in a way
that they equal one hundred. After many tries, I got four ways. Here they
are:
96/3+75-8-2-1+4 = 100
48/2+56+9+7+3+1 = 100
76+45-8-3-9-2+1 = 100
25 X 4+9+8-7-6-3-1 = 100
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From: CynTeach@aol.com
Date: Fri, 15 Dec 1995 14:08:27 -0500
To: ruth@mathforum.org
Subject: Elem Problem of the Week 12/11-12/15
These are the solutions found by students of Mrs. Bach's 5th grade at Joyce
Kilmer School in Mahwah, NJ 07430
Joe Baxley
8 x 5 +6 x 2 + 9 -3 +7 -4 - 1= 100
**need parentheses (8 x 5 +6) x 2 + 9 -3 +7 -4 - 1= 100
6 x 9 x 2 - 8 - 7 + 5 + 4 - 3 + 1=100
9 x 4 x 2 + 8 + 6 + 5 - 1 + 7 + 3 =100
7 x 3 x 2 + 9 x 8 / 4 - 6 + 8 - 5 + 1 =100
**need parentheses (7 x 3 x 2 + 9 )x( 8 / 4) - 6 + 8 - 5 + 1 =100
4 x 6x3 +9+8+7+5-2+1= 100
5 x 9 + 64 - 8 + 2 - 7 + 1 + 3 =100
9 x 8+7+6+5+4+3+2+1=100 Jessica Terry
98 + 2 - 5 - 3 - 4 + 6 + 7 -1=100 Jessica Kreusch
4 x 6 x 3 + 9 + 8 + 7 + 5 - 2 + 1 = 100
Jenna Beatrice 9 x 7 x 2 - 8 - 6 - 5 - 4 - 3 x 1 =100
Carolyn Weiss 98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
Jessica Ross 94 + 7 + 8 + 6 - 5 - 13 + 2 + 1 = 100
George Remo 23 x 4 + 9 + 7 - 8 + 5 + 1 - 6 = 100
Amy Killough 67 + 12 + 9 - 4 + 3 + 5 + 8 = 100
Jessica Cohen 5 x 4 x6 -9 -8-7+3+2-1= 100
Mrs. Bach's 5th grade at Joyce Kilmer School in Mahwah, NJ 07430
Joe Baxley (7 equations), Jessica Terry (1 equation), Jessica Kreusch (2
equations), Carolyn Weiss (1 equation), Jessica Ross (1 equation), George
Remo (1 equation), Amy Killough (1 equation), Jessica Cohen (1 equation),
Jenna Beatrice (1 equation), Carolyn Weiss (1 equation)
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Date: Fri, 15 Dec 1995 13:10:43 -0400 (EDT) From: MARILYN TAHL
Subject: Re: Elementary POW 12/11-15
To: ruth@mathforum.org
our names are Matt Burke & Anita Minakyan we are in Mrs. Hirns fourth grade
at Munsey Park school Manhasset N.Y. 11030
Our answers are : 18 rearrangements
3+12+4+5-6-7+89=100
3+4+12+5-6-7+89=100
12+4+3+5-6-7+89=100
3+4+12+5-7-6+89=100
89+3-7+5+4-6+12=100
89+5-7+3+4-6+12=100
89+5-7+3+4+12-6=100
5-7+89+4+5-6+12=100
89+3-7+5+12+4-6=100
89+12+3+5+4-6-7=100
89+5-6+3+4+12-7=100
89+4-6+3+5+12-7=100
89-6+3+12+5-7+4=100
89+5-7+3-6+12+4=100
127/54+983/6=100
983/6+127/54=100
12+3+4+5-6-7+89=100
12+4+3+5-7-6+89=100
12+3+5+4-6-7+89=100
12+4+3+5-6-7+89=100
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Bonus Puzzler
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This weeks bonus puzzler:
Mike D., Julia C., Nick S.
Fourth Grade
Bagnall School, Groveland, MA
They all got the same answer: 1
8 10
6 7 5
3 4 9 2
Nick figured out immediately that the 10 had to go next to the eight
because the only other choice would be seven and that would leave numbers
that were to small to make all lines the same.
Mike and Julia tried putting the 7 next to the 8 and the 10 on the third
row in the middle but soon figured out that wouldn't work without repeating
some of the smaller numbers so then they put the 10 next to the 8.
After they knew what each line added up to, they did some trial and error
work until they had placed all the other numbers.
- Hilary Seager
Hi Ruth,
I have another student who completed the bonus puzzler. Meghan R.
Grade 4
Bagnall School, Groveland
She worked it out the same way as Mike D. and Julia C. She tried putting
the 7 next to the 8 but found that wouldn't work, so she figured the 10 had
to go by the 8 and then just worked out which of the other numbers went
where to get rows of 18. Her solution is below.
1
8 10
6 7 5
3 4 9 2
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