Fill in the missing numbers with the digits 1 to 9. A diamond shape in the middle means that the four numbers around it add to 20.
Each uses a different way to add to 20, if there is already 1 + 3 + 7 + 9, then there will not be another using the digits 1, 3, 7 and 9 (in any order).
The same digit isn't allowed to touch, even diagonally.
Hint
The answer is 4 digits long, so what must G equal?
Answer
423 + 675 = 1098.
Reasoning
Remembering that:
even + even = even
odd + odd = even
even + odd = odd
To discuss individual letters, it's easiest to represent the sum as:
A B C
D E F +
————————
G H I J
A + D has to be over 9, which means that G = 1.
B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).
The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).
Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.
A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.
I is the only remaining odd number, so I = 9.
Which means that B = 2.
Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.
Therefore, A and D are 4 and 6 (but we don't yet know which is which).
Since the top row's digits have to add to 9, A can't be 6, so A = 4, making C = 3.
This makes the sum 423 + 675 = 1098.
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Puzzle 4
Which of the four shapes comes next in this sequence:
Reasoning
The shapes are the spaces between the digits in the numbers 27, 28, 29, and 30, therefore C is the correct answer, as it is the space between the digits in the number 31.
