FILE No.156Unsolved
Grid streets are laid out in a 4 × 4 block pattern. From the lower left to the upper right, you move only right or up.
How many shortest routes are there?
If you get stuck, open the hints one at a time, in order.
How many times do you move right, and how many up?
The order of the 8 moves is the route.
It is the number of ways to choose 4 from 8.
How many shortest routes are there?
Choose the answer closest to the truth.
70
The answer is "70."
You make 4 moves right and 4 moves up, 8 moves in all. Choose which 4 of the 8 moves are "right." Choosing 4 from 8 gives 70 ways.
16 and 256 come from simply multiplying the choices at each step, and do not use the condition "four of each."
Because you try to trace and count the routes on the map one by one.
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