Treasure chests

Use every number once.

Take a number from the first chest.

Add it to a number from the second chest.

Take the right answer from the third chest.

Now write your sum.

Repeat this until all the numbers are used up.

Pyramid

Age 14-16

The area of an inclined face of a square-based pyramid is equal to that of a square drawn on the vertical height of the pyramid.

What angle does the inclined face make with the base of the pyramid?

Brainteaser solutions from page 30

Treasure chests

9 + 8 = 17; 7 + 24 = 31; 18 + 17 = 35; 5 + 11 = 16; 14 + 13 = 27

Pyramid

The inclined face makes an angle of very nearly 52 LESS THAN with the base of the pyramid. The cosine of the required angle OPH is ap. The square on OH equals DOAB, so h2=ap. Using Pythagoras, in DPHA, HA2 = 2a2. In DOAH, OA2 = h2 + 2a2 = ap + 2a2. in DOAP, OA2 = p2 + a2.

So a2 + ap - p2 = 0. Dividing through by p2, and solving for ap, gives ap approximately 0.62. Angle OPH is therefore just under 52 LESS THAN .