ID 935

The first person is 100 cm tall.

Each subsequent person is 20% taller than the person before.

What will be the height of the fifth person?

ID 966

ID 993

ID 1000

ID 1274

ID 1282

ID 1880

ID 2032

The sum of the digits of a two-digit number X is Y.

The sum of the digits of X^{2} is Y^{2}.

Find X.

ID 2145

ID 2225

ID 2242

Make two fractions with all the digits from 0 to 9.

Use each digit once.

They add up to exactly 1.

What is one of the fractions?

ID 3541

ID 3719

ID 3743

ID 3794

ID 3846

ID 4025

If X^{Y} = 1024 and both numbers are integers, which of the following could not be a value of X nor Y?

ID 4091

ID 4160

ID 4167

ID 4378

ID 4687

Savin's problem:

Using each of the digits 1,2,3, and 4 twice, write out an eight-digit number in which there is one digit between the ones, two digits between the twos, three digits between the threes, and four digits between the fours.

How many such numbers?

ID 4705

ID 4786

What is the sum of the first 100 prime numbers?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

ID 5001

The average of 99 consecutive numbers is 99.

What is the average of the nine smallest of these numbers?

ID 5060

The natural numbers are the counting numbers, like 1, 2, 3, et cetera.

An even number is a natural number which is "evenly divisible" by two.

An odd number is a natural number which is not a multiple of two.

Which statement is correct?

ID 5061

ID 5140

A magic square is an arrangement of integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the diagonals, all add up to the same number.

Place numbers 13, 14, 15, and 16 in the square to make a magic square.

Which number do you place in the top left cell?

ID 5222

Leslie Green asks:

What is the next number in the sequence?

**0, 3, 1, 4, 2 **

(NOTE: It is a single sequence and not two sequences interleaved.)

ID 5426

Shakuntala Devi was undoubtedly the most brilliant arithmetic mental calculator of all time. In 1977 she mentally calculated the 23^{rd} root of a 201 digit number in a mere 50 seconds. She toured the world showing how she could do calculations faster than they could be entered into and solved by the computers of the day.

The problem for you is much simpler: Evaluate (without using a calculator) the 20^{th} root of the 11 digit number consisting of 1 followed by all zeros.

Author: Leslie Green

ID 5836

ID 5897

ID 6219

The numbers

129

CXXIX

10000001

81

all have the same value.

Why is CXXIX the odd one out?

Author: Leslie Green

ID 6286

ID 6762

Present 100 as a sum of positive integers such that their product is at its maximum value.

How many numbers do you use?