Question

Find all the numbers for each shape

Answer 1

Answer:

• 1 = pentagon
• 2 = diamond
• 3 = square
• 5 = circle
• 6 = rectangle
• 7 = oval
• 8 = triangle
• 9 = hexagon
• 10 = trapezoid

Step-by-step explanation:

Each half of a hanger divides the total weight in half. The right-most vertical has a total weight of 80/16 = 5. It consists of a square and a diamond, and we know the square is 1 more than the diamond. That means 2 diamonds weigh 5 -1 = 4. A diamond weighs 2, and a square weighs 3. The other half of that balance is a circle, which weighs 5.

The total of a square and oval is 10, so the oval is 10 -3 = 7. The two trapezoids weigh 20, so each is 10.

The second vertical from the left is a circle and diamond which will weigh 5+2 = 7. That makes the sum of a pentagon and rectangle also be 7. The 7+7 = 14 below the square on the left branch makes the total of that branch be 14+3 = 17, which is also the sum of the triangle and hexagon.

The weight below the rectangle at top left is 17+17 = 34, and the weight of that entire branch is 40. Thus the rectangle is 40-34 = 6, which makes the pentagon 7-6 = 1.

We require the sum of the triangle and hexagon be 17, with the triangle being the smaller value, and both being 9 or less (the trapezoid is the only figure weighing more than 9). Hence the triangle is 8 and the hexagon is 9.

The weights are summarized in the answer section, above.