## How many addition signs should be put between digits of 987654321

How many addition signs should be put between digits of 987654321 to equal 99? Where should they be placed? Time to solve 10 minutes.

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Submitted by Atanu Chaudhuri on Thu, 14/01/2021 - 23:47

Submitted by Atanu Chaudhuri on Mon, 11/01/2021 - 23:54

Cherry in the glass puzzle: Move 3 matchsticks to take the cherry out of wine glass. Second puzzle is harder: Move 2 matchsticks to take the cherry out.

Submitted by Atanu Chaudhuri on Sun, 10/01/2021 - 22:10

Move 2 matches to make 6 squares and move 8 to make 6 squares. Total time to solve the pair of challenging matchstick puzzles is 20 minutes.

Submitted by Atanu Chaudhuri on Fri, 08/01/2021 - 22:55

The leftmost digit of a natural number at least 7 digit long is 3. When the leftmost digit is dropped, the number formed by the rest of the digits becomes $\frac{1}{5}$th of the original number. What is the product of the non-zero digits of the original number?

**Hint:** Solve this 8th hard number system question for CAT using the very basic concepts intelligently.

Submitted by Atanu Chaudhuri on Wed, 06/01/2021 - 22:12

Cube of a number exceeds its product with two other numbers by 2, the cube of the second number is less than their product by 3 and the cube of the third exceeds their product by 3. Find the lowest of the three numbers.

Solve this 7th hard number system question for CAT quickly by mathematical reasoning based on indices concepts and inequality analysis.

Submitted by Atanu Chaudhuri on Tue, 05/01/2021 - 20:50

The product of a two digit number and a second number formed by reversing the digits of the first is 2430. Find the lower number. In solving this 6th hard number system question for CAT, mathematical reasoning based on factors multiples concept provided quick systematic solution...

Submitted by Atanu Chaudhuri on Mon, 04/01/2021 - 12:24

If 495 is subtracted from a 3-digit number with its digits reversed, result will be the original number. Sum of the digits of the number is 12 and sum of all pairwise products of its digits is 41. Find the number.

For quick solution of the 5th hard number system question for CAT, limit the possible values of the digits by identifying breakthrough conditions and enumeration using the given conditions....

Submitted by Atanu Chaudhuri on Sun, 03/01/2021 - 22:14

The sum of thousands and tens digits in a 4 digit number is 4, the sum of hundreds and units digit is 15, and units digit is greater than the thousands digit by 7. Among all such numbers satisfying these conditions, find the number, the sum of product of whose thousands digit and units digit and hundreds digit and tens digit is the least.

For quick solution of this 4th hard number system question for CAT limit the possible values of the digits by variable linking of the conditions...

Submitted by Atanu Chaudhuri on Sun, 03/01/2021 - 16:15

Denominator of a fraction is less than the square of the numerator by 1. If 2 is added to both, the fraction will be more than $\frac{1}{3}$. And when 3 is subtracted from both, the fraction remains positive and is smaller than $\frac{1}{10}$. Find the fraction.

For quick solution of this 3rd hard number system question for CAT, explore deeply inequality analysis and inequality algebra...

Submitted by Atanu Chaudhuri on Fri, 01/01/2021 - 18:12

What two digit number is less than the sum of squares of its digits by 11 and exceeds their doubled product by 5?

For quick solution of the 2nd hard number system question for CAT, discover the breakthrough information from the given resources...