It’s not too hard to form the number 9 using three 3’s and any of the four standard
mathematical operations +, –, × and ÷. But can you come up with four different
solutions, each of which uses only one of the four operations? (Other standard
mathematical symbols can be used as needed.)
= 3 + 3 + 3
Equations to solve in your
Is this a joke? Not if you can
multiply the first equation by 6,751 and the second by 3,249 in your head, and
not if you use a second, simpler method.
Which is bigger, or ?
Don’t even think about using
a calculator for this one.
According to Waring’s theorem, any positive integer can be represented as the sum of nine
or fewer perfect cubes (not necessarily distinct).
instance, 89 can be represented as the sum of four perfect cubes: 27 + 27 + 27
+ 8 = 89.
you express 239 as a sum of nine or fewer perfect cubes?
are 29 students in Miss Spelling’s class. As a special holiday gift, she bought
each of them chocolate letters with which they can spell their names.
Unfortunately, some letters cost more than others — for instance, the
letter A, which is in high demand, is rather pricey; whereas the letter Q,
which almost no one wants, is relatively inexpensive.
price of the chocolate letters for each student in her class is shown in the
AIDEN – 386
ARI – 209
ARIEL – 376
BLAIRE – 390
CHARLES – 457
CLARE – 334
DEAN – 317
EARL – 307
FRIDA – 273
GABRIEL – 410
IVY – 97
KOLE – 249
LEIA – 317
LEO – 242
MAVIS – 246
NADINE – 453
NED – 236
PAUL – 167
QASIM – 238
RACHEL – 394
RAFI – 231
SAM – 168
TIRA – 299
ULA – 148
VERA – 276
VIJAY – 179
WOLKE – 272
XAVIER – 346
ZERACH – 355
much would it cost to buy the letters in your
A prisoner was thrown into a
medieval dungeon with 145 doors. Nine, shown by black bars, are locked, but
each one will open if before you reach it you pass through exactly 8 open
doors. You don’t have to go through every open door but you do have to go
through every cell and all 9 locked doors. If you enter a cell or go through a
door a second time, the doors clang shut, trapping you.
The prisoner (in the lower
right corner cell) had a drawing of the dungeon. He thought a long time before
he set out. He went through all the locked doors and escaped through the last,
upper left corner one.
What was his route?
Ask a friend to pick a number from 1 through 1,000. After asking him
ten questions that can be answered yes or no, you tell him the number.
What kind of Questions?
What is the sum of the following?
432 + 432 + 432 + 432 + 432 + 432 + 864 + 864
Tom was born on Thanksgiving Day.
On his seventh birthday, he noticed that Thanksgiving had never fallen on
his birthday. How old will he be when he finally has a Thanksgiving birthday?
A plywood sheet is 45 by 45
inches. What is the approximate diameter of the log the sheet was made from?
The diameter d of a circle equals ,
where C is the circumference, but
please do not make a mistake. The diameter of the log is not .