# numbers want to cross a river, but their sum must be a square number

In the world of numbers, numbers 1 to 9 want to cross a river,
They have a boat which can take 1 to 3 numbers,
But sum of the numbers must be a square number.
The boat can not sail back itself, so there must be some numbers to sail back.

Plan minimum number of trips in such a way that all the numbers can cross the river.

I use Microsoft Clip art organizer to search the individual pictures (boat and man) then compose the picture.

• Just a minor note - your sails are hovering over the boat without being attached. – boboquack Jan 27 '18 at 5:14
• @boboquack maybe number land is highly technological and they invented levitating sails 0_0 – greenturtle3141 Jan 27 '18 at 16:44

The minimum is

7 crossings

This is achieved by:

Send 2+5+9 = 16
Bring back 9
Send 3+4+9 = 16
Bring back 9
Send 1+7+8 = 16
Bring back 1
Send 1+6+9 = 16

The minimum is

9.
The largest possible square that is the sum of 3 numbers is 16.
Therefore the only trips are 16, 9, 4, and 1. which can be done with the following:
First take 9, 5, 2, and bring back the 9.
Then take 8, 7, 1, and bring back 7, 2.
Next take 9, 7, and bring back the 9 again.
On the fourth trip over, take 9, 4, 3, and bring back the 1.
Finally take over the 6, 2, 1.

• The boat can not sail back itself. – Jamal Senjaya Jan 27 '18 at 4:05
• @JamalSenjaya fixed. – Herb Wolfe Jan 27 '18 at 4:30
• +1 for your effort, but sp3000 have the minimum trip. – Jamal Senjaya Jan 27 '18 at 4:51