Elementary POW, October 14-18,1996
Elem POW Problems || Sept-Nov '96 Problems || Elem POW Main Page
Sue walks upstairs one step at a time; Michael goes up two steps at a time; Phy, who is on the track team, goes up 3 steps at a time. If each person starts with his (or her) left foot on the first step of the stairs, 1. Which will be the next step on which all three tread? 2. Which will be the first step on which each will tread with his (her) right foot? 3. On which step will all three tread with their right foot?This week's mentors are from Anne Sandler's Algebra Classes at Smoky Hill High in Aurora, Colorado.
Huw Wilkins, age 9, grade 4 Home School, Tasmania, Australia. Student: Vinay aggarwal Teacher: Paul Nass School: 4th Grade, Georgetown Day School, Washington DC Greg Kolb , Grade Three Jackson School Elizabeth Pack, Justin Weiss, Robbie Birge-Osborne, Nathan Strauss, and Alex Tuchel-Veyhl Third Grade, Forsyth School, St Louis Missouri. The Fab 5-C (Phy Chauveau) Germantown Academy Mrs. Chauveau's 5th Grade Class Fort Washington, PA Jamie Tansey and Helen Snodgrass 5th grade Ms. Mitra's class St. Patrick's Episcopal Day School Washington, DC Jenny Rector, 5th grader Garrison Elementary School in Dover, New Hampshire. Lauren, Katey, Claire, Daina, Tim and Stephen - Grade 4 Drexel Hill School of the Holy Child, Drexel Hill, PA Rebecca Martin, Third Grade Marianne Blair's class George L. Hess Educational Complex Mays Landing, NJ 08302 Jill Smith, Fourth Grade Mrs. O'Connor's math class Titus Elementary School Warrington, PA. Diana M., Rachel T., Colleen C., Melanie B., Lauren G., Monica R., Kevin M. and Zach B. Miss Colwell's 6th Grade Class Oak View Elementary School Fairfax, Virginia Mrs. Gail Lauinger's 5th grade Mendocino, California All students from: Bagnall School, Groveland, MA Bobby Tucker Grade 6, Ms. Lalumiere Kerry Beddeos Grade 6, Ms. Lalumiere Alex Fitzgerald, Thomas Dunn, Russell Six, Jason Dolan Grade 3, Miss Seager Ben Jorgensen and Chris Knox, Grade 5 Mrs. Hamilton Garrison Elementary School, Dover,NH Scott Sacra Mrs. Trudell's 3rd grade Center School, Stow MA Rebecca Martin, Third Grade Teacher: Marianne Blair George L. Hess Educational Complex Mays Landing,NJ 08302 Ben Jorgensen and Chris Knox, Grade 5 Mrs. Hamilton Garrison Elementary School, Dover,NH Daniel Ain Paul Nass (teacher) Georgetown Day School Bryan Love and Sam Harrison Teacher: Janice Temple Udit Garg, Grade 4 Teacher: Paul Nass Georgetown Day School (GDS) Zack L., Gi-Soo, Scott C., and Samantha D. Peter L., Heming X., and Alia C. Robby R., Brian L. Teacher: Mark Trama
Student: Vinay aggarwal
Teacher: Paul Nass
School: 4th Grade, Georgetown Day School, Washington DC
e-mail: darshan@erols.com
I made a table like the one below, where L=left foot, R=right foot,
S=skip
Step Sue Michael Phy
1 L L L
2 R S S
3 L R S
4 R S R
5 L L S
6 R S S
7 L R L
Question 1: All 3 tread on step 7 as seen above.
Question 2: Sue is on step 2, Michael is on 3, and Phy is on 4 with right
foot.
Question 3: Based on the table above Sue's right foot will always be on
an even step but Michael will always be on an odd step. So they can not
tread on the same step with their right foot.
On the 13 step all the people will be on their left foot.
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From: jwilkins@tassie.net.au (John Wilkins)
answer from Huw,
1. They all tread on step 7 .
2. Sue will step on the 2nd step
with her right foot , M ichael 3rd and Phy 4th.
3.There is no step the same that they
can all tread on with their right foot .
I worked it out by making a table
FOOT SUE MICHAEL PHY
l 1 1
1
r 2 3
4
l 3 5
7
r 4 7
10
l 5 9
13
r 6 11
16
l 7 13
19
r 8 15
22
l 9 17
25
Huw Wilkins,age 9, grade 4, Home School, Tasmania, Australia.
Wilkins/Forster family
Crooked Tree Point.Cygnet.
Tasmania.Australia 7112.
ph.[002] 951456
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Mrs. Gail Lauinger's 5th grade
Mendocino, California
We had two different interpretations of the problem, so we sent the best
example of each.
Interpretation 1
We drew steps with signs on them such as Sr, (Sue right) and the next step
that each of their right foot landed on together we wrote down for number
1. For number 2 we did the same thing except we wrote their individual
first right foot steps.
1. Step seven.
2. Sue step 2 Michael step 3 Phy step 4
3. It has to be even, because Sue"s right always goes down on even.
Michael however steps on no evens so it
is impossible.
Interpetation 2
1. S 1 2 3 4 5 6 7 8 9 10 Step 6
M _ 2 _ 4 _ 6 _ 8 _ 10
P _ _ 3 _ _ 6 _ _ 9 _
2. S L R _ _ _ _ _ _ Sue step 2
M _ L _ R _ _ _ _ Micheal step 4
P _ _ L _ _ R _ _ Phy step 6
1 2 3 4 5 6 7 8
3. S L R L R L R L R L R L R Step 12
M _ L _ R _ L _ R _ L _ R
P _ _ L _ _ R _ _ L _ _ R
1 2 3 4 5 6 7 8 9 10 11 12
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