MS 131 : a2

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sivakrishnan2408

28 May 2023

School

Husson University

Department

Mathematics

Course

MS 131

Professor

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Logic Problem Solving



Logicproblemstendtoboildownto“Thinklogicallyandtryeverythinguntilsomething

sticks.”Thetricktosolvingthemtobreakthemdowntotheirsimplestparts.Don’ttryto

keeptrackofitallinyourhead,andhaveaplan.



ThePlan

1. Readtheproblem/promptcarefully.Payattentiontothedetails

2. Statewhatyou’retryingtoaccomplish.

3. Statewhatyouneedtoknowinordertoreachthatgoal.

4. Breaktheproblemdowntoitssimplestparts.

a. Makeasimpler/smallerscaleequivalentifapplicable.

b. Writedowneverythingyouknowabouteveryaspectoftheproblem

5. Drawdiagramsandreframetheproblem.

a. Saytheproblemaloud

b. Explainittoafriend

c. Lookitoverslowlywhilereadingitaloud

d. Drawapicture

e. Makeamodel

6. Worktowardssolvingtheproblemonestepatatimewhileshowingallyourwork

andassumptions.

a. Lookforpatternsandtrends

b. Lookforobvioussolutions

c. Trywhatevercomestomind

7. Repeatsteps16invaryingordersuntiltheproblemissolved.



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Example:Pascal’sTriangle

1

11

121

1331 

14641

15101051



Findthenextlineinthesequence(let’ssolvethistasktogether)



1. Readtheproblem/promptcarefully.

2. Statewhatyou’retryingtoaccomplish.

a. I’mtryingtofindthenextlineinthesequence.

3. Statewhatyouneedtoknowinordertoreachthatgoal.

a. Ineedtoknowthepattern.

4. Breakitdownintoitssimplestparts/smallestscale

a. 1

11

121

5. Reframetheproblem

a. 



6. Worktowardssolvingtheproblemonestepatatimewhileshowingallyourwork

andassumptions.

a. There’salwaysa‘1’ontheedge

b. Theinsidehastwodots;thesumoftwoones.



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c. Whatdoesthenextlinehave?

i. 1

11

121

1331

d. Two‘3’s.Thesumof‘1’and‘2’whichhappentobeaboveeach‘3’.

e. Tryadding‘1’and‘3’together,‘3’and‘3’together,and‘3’and‘1’together.

i. “464”

f. Comparetothenextlineinthesequence

i. 14641

g. Hey,itfits!Ijusthadtoadd‘1’totheedges.

h. IfItestthepatternfortherestofthesequenceeverythingmatchesandIget‘1

615201561’asthenextlineinthesequence

7. ‘1615201561’isthenextlineinthesequence.Problemsolved.



Additionalquestionsforyou:

● LabeltherowsofthePascaltrianglebyindicesn=0,n=1,n=2,…



● If“1XY………….YX1”istherown=20,

● Findx



● Findy



Let’sgeneralizethisproblem.

● If“1XY………….YX1”isthen^throwofthetriangle,whatarethevaluesofx

andy?



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