Cool Math Puzzles

Instructor: Jessica Keys
Why not try a little mental exercise with this selection of eight fun math puzzles? All you need is your brain and a sense of logic. But beware, some of these are tricky! (If you get stumped, don't worry! This article includes all the answers at the end.)

Puzzle #1: Mother's Day

The Seashell Hotel set up a lovely buffet for Mother's Day. Among other things, the chef has whipped up a marvelous chocolate cherry cheesecake. Out on the patio, two mothers and two daughters are dining on three pieces of cheesecake, with one piece per person. How is this possible?

Puzzle #2: I, Robot

Can you replace the letters in this equation with numbers to make a correct mathematical expression?

(R+O+B+O+T)³ = ROBOT

Puzzle #3: That Certain Something

Here's a number: 8549176320. It looks like a random jumbly number, but it's actually quite special. Can you figure out why?

Puzzle #4: Game of Fours

Hard to believe, but it's possible to get every integer between 0 and 8 by using four 4's (no more, no less, but decimal points are allowed) and the common math operators: addition, subtraction, multiplication, division, square root and the factorial (e.g. 4! = 1*2*3*4 = 24).

How many can you get?

Puzzle #5: Ugh!

Did you know? In math, there is a symbol you can stick between the numbers 7 and 8 that'll give you a number larger than 7, but smaller than 8. What is it?

Puzzle #6: Martian Math

'Decimals? Bah! That may be how math works on your Earth, but here on Mars everyone knows one half of five is three exactly,' grumbled Jim the Martian, as if he had just heard the most ridiculous thing in his life.

If one half of five is three on Mars, and assuming this strange proportion is the rule, what is one third of ten?

Puzzle #7: Wacky Factory

Doctor Crumbs has got her manufacturing business down to a science. Now one and a half of her lawn chair making-machines can produce exactly one and a half lawn chairs every one and a half hours. Unfortunately, this silly math has confounded her potential investors. Can you help her figure out how many lawn chairs one machine can produce in one hour?

Puzzle #8: Crazy 8s

Can you add eight 8s to get the number 1000?

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Here are the answers to all the puzzles. Don't look unless you're really stumped!

Puzzle #1: Out of the two mothers, one is actually a grandmother. This means one of the mothers is both a mother and a daughter. So technically, the table seats two mothers (the grandmother and the mother) and two daughters (the mother and her daughter).

Puzzle #2: If R = 1, O = 7, B = 5, O=7, T = 6, then (1+7+5+7+6)³ = (26)³ = 17576.

Puzzle #3: 8549176320 is all the single digits (0-9) rearranged in alphabetical order: 'Eight, Five, Four, Nine, One…'

Puzzle #4: Some solutions for 0 to 8 are:

(4+4) - (4+4) = 0 (4+4) / (4+4) = 1 (4/4) + (4/4) = 2
((4+4) + 4)/4 = 3 4(4-4) + 4 = 4 ((4*4)+4)/4 = 5
4(.4) + 4.4 = 6 (44/4) - 4 = 7 4 + (4.4 - .4) = 8

Of course, you don't have to stop at just 8! For a challenge, see how far you can go using these rules.

Puzzle #5: A decimal point! 7.8 is larger than 7 and smaller than 8. Try this one out on your friends if you really want to annoy them. (No more trick questions, promise!)

Puzzle #6: We know that according to Martian rules, 1/2 * 5 = 3 (Here on Earth, the real answer is 2.5). We want to know what 1/3 * 10 would be using the same wonky proportions.

  • Try setting up the problem like so: 1/2 * 5 = 3.
  • But we want to know about thirds. So multiply both sides of the equation by 1/3. You will end up with 1/6 * 5 = 1. Getting there!
  • Turn that 1/6 into 1/3 by multiplying both sides by two and you will end up with 1/3 * 5 = 2. So, one third of five is two…
  • Now all you have to do is double the whole thing (multiply both sides by two again) to figure out what one third of ten would be. (It is, of course, four.)

Puzzle #7: All you have to do is work out the rate per hour (r) using this formula: x Machines * y Hours * (r) = z Lawn Chairs.

The starting expression is 1½ * 1½ * (r) = 1½. Isolate r by dividing out the 1½ * 1½, where it will then become the denominator on the other side:

  • r = 1½ / (1½ * 1½)

You can simplify this fraction by canceling out the 1½ in the numerator with a 1½ in the denominator. This leaves you with:

  • r = 1 / 1½, or r = 1 / (3/2), which becomes r = 2/3.

So, one lawn chair machine can make 2/3rds of one lawn chair in one hour. How silly!

Puzzle #8: To get 1000 by adding eight 8s, try 888 + 88 + 8 + 8 + 8. It helps if you remember that 8 x 5 is 40, a number that ends in zero. Therefore, dividing the eight 8s into five portions will get you a number that ends in zero.

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