# 16 number puzzles on a blackboard

I have left you some number puzzles on the blackboard. Solve them and let me know what they spell.

Hint:

The final answer is two words and is something from Harry Potter

The individual answers, starting from top left and moving right, are

19 (subtract 19 each time)
20 (multiply by 5)
19 (a^2 + b)
18 (sum of 2 opposite triangles)
7 (multiply 2 vertices, divide by left vertice)
8 (square of opposite number minus 1)
11 (a*b + a + b)
19 (circle is 4, triangle is 2, rectangle is 1)
14 (base 8)
17 (rotate 180 degrees)
13 (sum of opposites minus bottom right gives top left)
0 (just calculate)
3 (just algebra)
14 (just calculate)
18 (sum of two left diagonals gives number on top)

Then use A-Z = 0-25.

• Correct. You got all of them right. – eyl327 Mar 1 at 13:37
• Thanks! Fun puzzle. :) – Jens Mar 1 at 13:50
• If you want to solve more, I've posted some letter puzzles. Some are similar, others are new. puzzling.stackexchange.com/questions/94388/… – eyl327 Mar 1 at 14:16

Solving the number puzzles:

1. $$19$$ (descending multiples of 19)

2. $$20$$ (multiplying the left number by 5 to get the right one)

3. $$19$$ (square of first number plus second number gives third number)

4. $$18$$ (each outer number is the sum of the two inner numbers furthest from it)

5. $$7$$ (bottom left of each triangle is the product of the other two divided by 2)

6. $$8$$ (each larger number is the square of the opposite smaller number minus 1)

7. $$11$$ (each larger number is the sum of the two adjacent smaller numbers)

8. $$11$$ (add 1 to everything and this becomes simply products)

9. See Jens's answer - I didn't manage to get this one.
10. $$14$$ (base 8 on the left, base 10 on the right)

11. See Jens's answer - I didn't manage to get this one.
12. $$13$$ (both diagonals give the same sum)

13. $$0$$ (direct calculation)

14. $$3$$ (solving the first two equations gives A=30 and B=10)

15. $$14$$ (direct calculation)

16. $$18$$ (moving from southwest to northeast by making each new cell the sum of the two touching it)

Turning the numbers into letters:

S T S R
G H K K
S N Q M
 C N R

The final step, motivated by the appearance of

no vowels, but quite a few letters that precede vowels, like S and N (this also explains the mysterious zero),

is to

add 1 to all the numbers (or Caesar-shift the letters by 1) to get:

T U T S
H I L L
T O R N
A D O S

yielding the solution.