Sujiko Puzzle – 1
In this small 2 by 3 Sujiko puzzle, use each of the numbers from 1 to 6 once in the six squares. The number in each circle must be the sum of the four squares that surround it.
THE CHALLENGE
Fill in this Sujiko puzzle.
EXPLORATION
How many different answers can you find?
Notes
THE CHALLENGE & EXPLORATION
Each column of numbers – the 2 and 6, the 1 and 3, and the 4 and 5 – can be reversed in the answer given below. This produces a collection of 2 x 2 x 2 = 8 possible answers, one of which is shown below.
The 1 and 3 must be in the middle column. Call the middle numbers A and B. Add things up in two ways. The sum of all the entries in the two 2 by 2 squares is 12 + 13 = 25. On the other hand, that sum is all six numbers (1 to 6) with the middle column counted twice – that is, the sum is 1 + 2 + 3 + 4 + 5 + 6 + A + B = 21 + A + B. This means 25 = 21 + A + B, or 4 = A + B. This forces A and B to be 1 and 3.
With the middle column being 1 and 3, that forces the sum of the two entries in the right column to be 9. We can only get 9 as 4 + 5 or 3 + 6, but the 3 is already used. Therefore the rightmost column is 4 and 5.
There are only two numbers, 2 and 6, remaining for the leftmost column, and they work.