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You may be familiar with all the problems, but I would like to introduce the fun of brain teasers and arithmetic/mathematics, and I would like to do it in the form of a series from time to time in the column ^_^
[Question example]
Children sit on benches in the auditorium. If there are 7 on each bench, then all but the last bench has 3 sit, and the last bench has no one on it. Also, if 5 people sit on each bench, 15 people cannot sit. How many benches are there and how many children are there?
In general, we use the concept of area or think in terms of line segments (line length). Can you come up with a solution other than the one given in the example above?
It is used when solving using area, but you try solve it not use do not the area diagram.
[Solution example]:
1 No change in number of bench
2 No change in number of children
[My idea]:
From 1, 2
(1) 15 people standing without being able to sit when 5 people sit on one bench.
(2) When there is a bench for 7 people, no one sit on one bench, and in the case for 5 people, 5does not sit.
(3) for 7 people bench, one has 3 people, in the case for 5 people, 2 people don’t sit.
From ①, ②, ③
15+5+2=22・・・④
When the 22 people in ④ were for 7 people, everyone was seated, so using this,
7 people is more than 5 people
7-5=2
this tells 2 more people could sit on the bench than 7 people bench, so we made use of the fact that 2 more people.
22➗2=11
The idea is that 22 people sit on 11 bench.
* Is it difficult to understand because it is explained in words (sentences)? Make it an image or a draw and think about it!
That is all for this time. After that, please pay attention to the end by yourself and try to give an answer to what is being asked.
☆ I'm looking forward to seeing your thoughts, impressions, and answers to this way of thinking.
