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On Friday I participated in an annual ritual now known as the Soifer Mathematical Olympiad, in which middle and high school students attempt to solve five increasingly difficult problems. I spent the morning in the room with the 140 contestants clarifying what they didn’t understand so I have a feel for what many of them were experiencing.

Here’s problem #1 (easy) so you have an idea what was going on:

Given numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. In a step, you may add or subtract 1 from any two of the numbers. Is there a series of consecutive steps that in the end produces ten equal numbers? (Go here for a complete set of problems. Solutions or critiques of your solutions provided upon request.)

Questions from the students included, “What am I supposed to do?” Answer: “If a series of steps can produce 10 equal numbers, show how. If it can’t, explain why.” Another question: “Do I add or subtract 1 to two different numbers?” “Answer: “What does the problem say?”

Bottom line: many of the students were in shock because it’s the first time in their educational experience that they’ve been asked to do something they can’t do. The math questions they are used to are on the order of, “Given a right triangle with legs 8 and 15, use the Pythagorean Theorem to compute the length of the hypotenuse.” 

Our problems require them to write an essay. Spoiler Alert! The answer to #1 follows: 

The sum of the given numbers is odd, and the allowed steps increase the sum by 2, decrease it by 2 or leave it unchanged. Hence, the sum remains odd. On the other hand, the sum of 10 equal integers is even, and therefore the equality of ten numbers cannot be achieved.

40 students got #1 right, meaning over 100 students didn’t solve #1 or anything else. This parting comment from a stunned 4th grader (a little younger than the target population!) sums it up:

What’s our lesson? Some of us would say, “Of course, it’s not by trying it’s by trusting Jesus to save us from our sins.” But it’s more than that. We are saved to something, not just from something. 

[Jesus] gave himself for us to redeem us from all wickedness and to purify for himself a people that are his very own, eager to do what is good. (Titus 2.14, NLT)

But as he who called you is holy, you also be holy in all your conduct. (1 Peter 1.15, ESV)

In the words of Dallas Willard, it’s not by trying, it’s by training. The students who wrote the top papers didn’t get there accidentally—they’ve been studying and practicing for years. To change the metaphor, if all the weight I can lift on a certain exercise is 50 pounds, trying harder won’t get me to 100 pounds. But over time, training will.

John Ortberg suggested that if you want to practice patience, for example, why not select the longer checkout line?! Memorizing and meditating on scripture for problem areas helps too. Change is not instant, but growth does occur over time…when we train.

And he said, “The kingdom of God is as if a man should scatter seed on the ground. He sleeps and rises night and day, and the seed sprouts and grows; he knows not how. The earth produces by itself, first the blade, then the ear, then the full grain in the ear. (Mark 4.26 – 28, ESV)

Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—his good, pleasing and perfect will. (Romans 12.2, NIV)