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Last week's question #117 was
What are the next two numbers in this pattern?
121, 441, 961, 691, 522, 652, 982, ____, ____
answer: 423, 163
they are the squares of the numbers 11,12,13,..
.written backwards eg 12*12=144 therefore 441
.... 17*17=289 therefore 982
18*18=324 therefore 423
19*19=361 therefore 163
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******Congratualations to all who entered!*******
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~ Winners for puzzle #117 ~
those who found a defendable solution
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answers 423, 163
*********** the hoped for reply (it was harder than I thought)
gordie lidstone
winfield elementary school - winfield, ab, tocopo
FATIMA, SUJATA
St. John's High School,stjohnsl@soochak.ncst.ernet.in
THOMPSON KWAKU NUNIFU,tknunifu@Ice.Lakeheadu.Ca
Barry Spence
Red Deer AB
era srebmun owt txen ehT: 423, 163
Grade 6 Gomes/Cheverie
Tallahassee Community School - Eastern Passage, N.S.
121 = 11X11 reverse order 121
144 = 12x12 reverse order 441
169 = 13x13 reverse order 961
196 = 14x14 reverse order 691
225 = 15x15 reverse order 522
256 = 16x16 reverse order 652
289 = 17x17 reverse order 982
324 = 18x18 reverse order 423
361 = 19x19 reverse order 163
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******* a creative approach! answers 423, 163
David Barry
I'm taught at home. I live in Corner Brook, NF, Canada.
I found the answer to this problem by putting all the
numbers backwards and then I found how much each number went
up by each time. Then I found the sequence 23, 25, 27, 29,
31, 33 etc. ect. ect.
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answer 442, 123
******* I am very impressed!
******* convoluted is the word .... I would not do this to you!
BCHS MATHOIDS
Baie Comeau High School - Baie-Comeau, Qc
The reasons: convoluted, but...
1 2 1} The last digits of the first series of four are all 1
4 4 1} The middle digit starts at 2, +2 =4, +2 =6, +3 =9
9 6 1} The first digit of starts at 1 +3=4,+5=9,+7 =16, but only
6 9 1} the last digit, 6 is recorded.
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5 2 2} The last digits of this second series of four are all 2
6 5 2} The middle digit starts at 2, now +3 =5, +3 =8, +4 (one more
than the series above, gives 12. We only record the last digit
of two digit numbers. This trait is also found for the first digit.
9 8 2} The first digit continues from 16 +9=25,+11=36,+13=49,+15=64,
Remember only the last digits are recorded, so 5,6,9,4.
*4 4 2} Therefore here the last digit must be 2
Therefore here the middle digit is 2 (from the last digit of 12)
Therefore here, the first digit is 4 (from the last digit of 64)
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*1 2 3} For this next series of four, the last digit must be 3
because the first series used 1, the second used 2...
For this series of four the middle digit is, as before, 2
The first digit continues from the first digit of 442.
64+17=81, and we record only the last digit of 81, 1
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answers 822, 163
********* A couple of half right answers:-
Jory, Monica,Erin,Kayla,Beth
Stephen, Drew,Charley,Kyle
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answers 1023, 1063
********* The similarities of these answers are interesting
but no rationale was given.
Dan Opperman, Braden Power, Gr. 6 (Mr. Harvie)
St. Benedict's School - Sarnia.
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