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Difficulty: 3 of 5 Latest: 3 equal products (in Numbers)
Lets take a number 12 as an example . It can be partitoned into three integer summands in 12 ways:
12=1+1+10
12=1+2+9
12=1+3+8
12=1+4+7
12=1+5+6
12=2+2+8
12=2+3+7
12=2+4+6
12=2+5+5
12=3+3+6
12=3+4+5
12=4+4+4

Multiplying the 3 members of each partitions results in 12 distinct numbers: 10,18,...60,64.

On the other hand the same treatment applied to number 13 produces a pair of equal results: 13=1+6+6=2+2+9 and 1*6*6=2*2*9=36 (a well known problem of children's ages).

Find the smallest number which has 3 distinct partitions into 3 parts, each of them with the same product.

Bonus: list all numbers below 1000 boasting this feature.

(No Solution Yet, 4 Comments) Submitted on 2018-11-21 by Ady TZIDON   
Difficulty: 2 of 5 Bonus: Faulty Scales (in Weights and Scales) Rating: 4.25
Good scales have equal arms (arms are the the things that connect the actual scale to the center), but in one grocery stall, the arms of the scale are not equal. Pending replacement, the manager wonders if he can give correct weight this way:

"I'll balance a 1-pound weight on the left with sugar on the right, and then I'll balance the 1-pound weight on the right with some more sugar on the left, and the sugar will add up to exactly 2 pounds."

Will it? What are other (assuming that the above works, it may not) ways of weighing 2 pounds of sugar, if you also have a lead shot with you to help weigh? (Note and hint: The lead shot has an unknown weight. You can make it whatever weight you choose. Remember, the arms aren't equal, and you need 2 pounds of sugar.)

(Solution Posted, 8 Comments) Submitted on 2004-05-23 by Victor Zapana   
Difficulty: 3 of 5SETI (in Sequences)
Posted on 2018-11-20 by Charlie (No Solution Yet, 3 Comments)
Difficulty: 1 of 5A non-algebra problem (in Numbers)
Posted on 2018-11-19 by Ady TZIDON (No Solution Yet, 4 Comments)
Difficulty: 4 of 5New word from two others (in Word Problems)
Posted on 2018-11-18 by Ady TZIDON (Solution Posted, 9 Comments)
Difficulty: 3 of 5All Primes (in Just Math)
Posted on 2018-11-17 by Danish Ahmed Khan (No Solution Yet, 2 Comments)
Difficulty: 3 of 5MOI of a magic square (in Just Math)
Posted on 2018-11-16 by Ady TZIDON (No Solution Yet, 0 Comments)
Difficulty: 3 of 5Sine of Squared (in Calculus) Rating: 5.00
Posted on 2018-11-15 by Danish Ahmed Khan (No Solution Yet, 5 Comments)
Difficulty: 2 of 5Plaintext in Order (in Word Problems)
Posted on 2018-11-14 by Charlie (Solution Posted, 1 Comments)
Difficulty: 2 of 5Rectangles 2 (in Shapes)
Posted on 2018-11-13 by Charlie (Solution Posted, 1 Comments)
Difficulty: 2 of 5The penultimate digit (in Just Math)
Posted on 2018-11-12 by Ady TZIDON (No Solution Yet, 2 Comments)
Difficulty: 3 of 5Too Small of an Angle (in Just Math)
Posted on 2018-11-11 by Danish Ahmed Khan (No Solution Yet, 0 Comments)
Difficulty: 4 of 5The Unit Square in the Circle (in Geometry)
Posted on 2018-11-10 by Danish Ahmed Khan (No Solution Yet, 1 Comments)
Difficulty: 2 of 53D rooks puzzle (in Just Math) Rating: 3.00
Posted on 2018-11-09 by Ady TZIDON (No Solution Yet, 3 Comments)
Difficulty: 4 of 5Tangent Ellipses (in Just Math)
Posted on 2018-11-08 by Danish Ahmed Khan (No Solution Yet, 2 Comments)
Difficulty: 2 of 5Not a common text (in Word Problems)
Posted on 2018-11-07 by Ady TZIDON (Solution Posted, 4 Comments)

Recently Posted Solutions:
Difficulty: 4 of 5New word from two others (in Word Problems)
Submitted By Ady TZIDON. Solution posted on 2018-11-21 01:16:30
Difficulty: 3 of 5Art is marching on.. (in Word Problems)
Submitted By Ady TZIDON. Solution posted on 2018-11-20 03:11:23
Difficulty: 3 of 5The trio (in Liars and Knights)
Submitted By Math Man. Solution posted on 2018-11-19 19:47:10
Difficulty: 2 of 5Plaintext in Order (in Word Problems)
Submitted By Charlie. Solution posted on 2018-11-18 12:53:44
Difficulty: 2 of 5Rectangles 2 (in Shapes)
Submitted By Charlie. Solution posted on 2018-11-18 12:52:29
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