Pattern?
Number Theory
Level
3
If statements below are true, then find the value if the ?
| 11 | X | 11 | = | 4 |
| 22 | X | 22 | = | 16 |
| 33 | X | 33 | = | ? |
36
18
Not enough information given
108
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1 solution
There is simply not enough information given here to conclude one answer.
18 is a popular answer given since 11X11=121=(1+2+1)=4, and 22X22=484=(4+8+4)=16, thus 33X33=1089=(1+0+8+9)=18
36 is also popular, multiple ways to show this, most common is 11X11=(1+1)(1+1)=4, 22X22=(2+2)(2+2)=16, thus 33X33=(3+3)(3+3)=36
64 is not as common, but can be shown by 11X11=2^(1+1)=4, 22X22=2^(2+2)=16, 33X33=2^(3+3)=64
Recently a student of mine showed 36 as answer in another way, he divided each answer by 30 and rounded, i.e. 11X11=121/30=4 (rounded), 22X22=484/30=16 (rounded), thus 33X33=1089/30=36 (rounded)
To date I have twelve justifiable solutions to this problem! All from HS students, so I am curious how many more this community will think of!!!