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# ACL-2022 | 字节跳动与新加坡科技与设计大学提出：基于演绎推理的数学解题

Question: In a division sum , the remainder is 8 and the divisor is 6 times the quotient and is obtained by adding 3 to the thrice of the remainder. What is the dividend?

Mathematical Expression: （（8×3+3）×（8×3+3）÷6）+8

1. 通过重复利用已有的结果计算，减少了总的计算步数。

2. 一步步的计算过程相对于 Seq2Tree 的生成更加可解释。

3. 生成是生成整个表达式，而不是单个 operator 或者是数字。这样的 constraint 在训练过程中使得模型要更加准确的得到整个表达式。

Question: There are 255 apple trees in the orchard. Planting another 35 pear trees makes the number exactly the same as the apple trees. If every 20 pear trees are planted in a row, how many rows can be planted in total?

Answer: 11.   Gold Expression:  (255 - 35) / 20.  Predicted Expression:  (255 + 35) / 20 Deductive Scores: Prob(‘255+35=290’) = 0.068 > Prob(‘255-35=220’) = 0.062

Question: There are 255 apple trees in the orchard. The number of pear trees is 35 fewer than the apple trees.  If every 20 pear trees are planted in a row, how many rows can be planted in total?

Prob(255+35=290) = 0.061 < Prob(255-35=220) = 0.067

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[2] Daniel, Kahneman. "Thinking, fast and slow." (2017).
[3] Amini, Aida, et al. "MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms." Proceedings of NAACL, 2019.
[4] Xie, Zhipeng, and Shichao Sun. "A Goal-Driven Tree-Structured Neural Model for Math Word Problems." Proceedings of IJCAI. 2019.