Math CentralQuandaries & Queries


Question from Jeff, a parent:

My son in the 5th grade was given a problem for extra credit and could use parents help. He was given the numbers 21, 13, 9, 6 and asked to use each number only once by +, -, /, x the numbers in any order to obtain an answer of 24.
After hours of work, I came up with (13 - 21) * (6-9), which was -8 *-3 = 24. The teacher gave him the extra credit but told him he didn't do it the right way. BUT she didn't have another answer. My question, is there another way to do this? It's been a long time since I was in college, but I think there is over 1,500 possible combinations using these for numbers and symbols.

Hi Jeff,

There is no right way to solve the game of 24 problems. The challenge is to find a correct solution, which you did! Perhaps the teacher wanted to see (21 - 13) × (9 - 6) = 8 × 3 = 24 but your solution is just as valid.

I assume you got the "over 1,500 possible combinations" from the calculation 4 × 4 × 3 × 4 × 2 × 4 but the string of symbols and numbers could start with a minus sign so I get twice that many. That is of course ignoring pairs of parentheses which add more to the number of combinations.


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