Which number is diametrically opposite to 7?
The number is 22.
(From the UK Association of Teachers of Mathematics book,
Eight Days A Week)
• What process did you use to work on and solve this puzzle?
Diametrically opposite: that means we can cut the total number
in half. So, the first half is 1-15, the second half is 16-20, so the 16 is
diametrically opposite to 1. 7=6+1, so 16+6=22.
• Could you create other extended puzzles related to this
one -- some possible, some impossible?
(Is there any value to giving your students impossible puzzles?)
30 students stand in a circle playing hiding game. The 12th
student who hides a treasure behind the students who is 90 degrees with him clockwise.
Which student is in front of the
treasure.
•What makes a puzzle truly geometric, rather than simply
logical?
People can draw a truly geometric shape to find a pattern and solve it without using logic. So it could be act-on.
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