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.

Calculation race

Ask your friend to write any two-digit number and multiply it manually by 3367.

You will always be able to get the answer before him/her without a calculator.

Example: If your friend chooses 53, then write 535353 and divide it by 3.

Thus, 535353/3 = 178451

Check: 53 x 3367 = 178451

Trick: Write the two-digit number thrice and divide it by 3.

Answer to previous question

The possible solutions to the question are:

98765 + 1234 = 99999

97864 + 2135 = 99999

96125 + 3874 = 99999

Today's question

 Make two numbers using each digit from 1 to 9 only once. The sum of the numbers must be 99999. Can you do it? There can be more than one possibility. Post your answers as comment.

Easy multiplication by 9

To multiply a number by 9, multiply it by 10 and then subtract the original number.

Example: To multiply 139 by 9, first multiply 139 by 10.

139 x 10 = 1390

Next subtract 139 from 1390.

1390 – 139 = 1251

Thus 139 x 9 = 1251

Answer to previous question

The answer to previous question is 4913. 4 + 9 + 1 + 3 = 17.

17 x 17 x 17 = 4913.

Today's question

I suppose a four-digit number. The cube of the sum of the digits is equal to the number itself. Can you say which is the number?

Answer to Wednesday's question

The number which gives the same result when multiplied by 5/4 and when added to 5/4 is 5.

Multiplying big numbers by 11

To multiply big numbers by 11, first multiply the number by 10 and then add the original number to the product.

Example: To multiply 9876 by 11 first multiply it by 10 (9876 x 10 = 98760)
Add 9876 to 98760 (9876 + 98760 = 108636)

Mysterious 24

If you square any prime larger than 3 and subtract 1, the answer will always be divisible by 24.

Example:  19 x 19 = 361, 361 – 1 = 360

360/24 = 15

Today's question

Today’s question:

Which number when multiplied by 5/4 gives the same result as when added to 5/4?

Post your answers as comment. The answer will be published on Friday.