Puzzles

Write the numbers 1 to 15 in a row. Underneath, write the same list without the first and last numbers. Continue this until you have just one number left.

Today's number is the sum of all the numbers you have written.

The odd numbers are written in a pyramid.

What is the mean of the numbers in the 23rd row?

The odd numbers are written in a pyramid.

What is the sum of the numbers in the seventh row?

\(p(x)\) is a quadratic with real coefficients. For all real numbers \(x\),

\(p(2)=34\). What is \(p(6)\)?

You start at A and are allow to walk left, right, up or down along the grid. The grid continues forever in every direction. After you have walked thirteen units, how many different locations could you be in?

Pick a three digit number whose digits are all different.

Sort the digits into ascending and descending order to form two new numbers. Find the difference between these numbers.

Repeat this process until the number stops changing. The final result is today's number.

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the numbers in the red boxes.

There are three cards; one number is written on each card. You are told that the sums of pairs of cards are 99, 83 and 102. What is the sum of all three cards?