Today's question

Find a three-digit number such that the number is divisible by each digit of the number and all the digits are prime. You can post your answers as comment.

Multiplying two-digit numbers by 11

To multiply a two digit number by 11, write the ones digit of the two-digit number at the ones place of the answer.

Add the ones and tens digit to get the middle number of the answer.

Write the tens digit of the number at the hundreds place of the answer.

Example:

To multiply 43 by 11, write 3 at the ones place of the answer.

Add the ones and tens digit (4 + 3 = 7), 7 is the middle number of the answer.

The tens digit 4 is in the hundreds place of the answer.

Thus, 43 x 11 = 473

Answer to previous question

The pairs are

(1,8),(7,2),(6,3),(4,5),(16,9),(15,10),(14,11),(13,12)

Today's question

Make the numbers from 1 to 16 as 8 pairs of numbers. The sum of each pair should be a perfect square. You can post your answers as comments.

Easy division by 9

A repeated pattern is produced when a number smaller than 9 is divided by 9.

Example:

1. 7/9 = 0.777... (This will work if the dividend is from 1 to 8 and the divisor is 9)

2. 86/9 = 0.8686... (This will work if the dividend is from 10 to 98 and the divisor is 99)

3. 5/99 = 0.0505... (This will work for dividends 1 to 9 and divisor 99)

4. 594/99 = 0.594594... (This will work for dividends 100 to 998 and divisor 999)

5. 74/999 = 0.074074... (This will work for dividends 10 to 99 and divisor 999)

6. 3/999 = 0.003003... (This will work for dividends 1 to 9 and divisor 999)

Answer to previous question

All cubes are in the form 7n + 1. That is, when 1 is added or subtracted from the cube, they will be multiples of 7.

                  

                  2x2x2 = 8 = (7x1) + 1

                  3x3x3 = 27=(7x4) - 1

                  4x4x4 = 64=(7x9) + 1

                  5x5x5 = 125=(7x18) + 1

Today's Question

The cube of any integer is in relation with 7. Can you find the relation?

Numerical Palindrome

A palindromic number is a number which reads the same forward and backward. 

• Write any whole number.
• Reverse its digits and add to the previous number.
• To this sum add the number formed by reversing the sum’s digits.
• Continue this process. Ultimately you will reach a palindromic number.

Example:

• Let’s start with 3659.
• Reversed number is 9563.
• Sum of the two numbers is 3659 + 9563 = 13,222.
• Continuing the process we get 13,222 + 22,231 = 33,453 (palindromic number).

Answer to previous question

Using eight 8s 1000 can be expressed as
888 + 88 + 8 + 8 + 8 = 1000
Congratulations to all those who got it right.

Today's question

Using eight 8s, try to get the value of 1000. Post your answers as comment.